Algebra 1 Unit 8 Test Quadratic Equations

What Is Parabola Graph

A parabola is a U-shaped curve that is drawn for a quadratic function, f = ax2 + bx + c. The graph of the parabola is downward , when the value of a is less than 0, a < 0. The graph of parabola is upward when the value of a is more than 0, a > 0. Hence, the direction of parabola is determined by sign of coefficient a.

Unit 8 Test Review Algebra

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Vertex Form Of Parabola Equation

The extreme point of a parabola, whether it is maximum or minimum, is called vertex of parabola. The parabola equation can also be represented using the vertex form. The vertex form of the parabola equation is represented by:

f = y = a 2+k

Here, is the vertex point of the parabola.

Similar to the standard form of the parabola equation, the orientation of the parabola in the vertex form is determined by the parameter a.

If the value of a is positive, the parabola graph is upwards.

If the value of a is negative, the parabola graph is downwards.

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Identify The Most Appropriate Method To Use To Solve A Quadratic Equation

We summarize the four methods that we have used to solve quadratic equations below.

Given that we have four methods to use to solve a quadratic equation, how do you decide which one to use? Factoring is often the quickest method and so we try it first. If the equation is or we use the Square Root Property. For any other equation, it is probably best to use the Quadratic Formula. Remember, you can solve any quadratic equation by using the Quadratic Formula, but that is not always the easiest method.

What about the method of Completing the Square? Most people find that method cumbersome and prefer not to use it. We needed to include it in the list of methods because we completed the square in general to derive the Quadratic Formula. You will also use the process of Completing the Square in other areas of algebra.

The next example uses this strategy to decide how to solve each quadratic equation.

Identify the most appropriate method to use to solve each quadratic equation.

• The solutions to a quadratic equation of the form ax2 + bx + c = 0, are given by the formula:

Common Core Algebra 1 Unit 8 Lesson 2 Answer Key

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Common Core Algebra 1 Unit 8 Lesson 1

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Solve Quadratic Equations Using The Quadratic Formula

When we solved quadratic equations in the last section by completing the square, we took the same steps every time. By the end of the exercise set, you may have been wondering isnt there an easier way to do this? The answer is yes. Mathematicians look for patterns when they do things over and over in order to make their work easier. In this section we will derive and use a formula to find the solution of a quadratic equation.

We have already seen how to solve a formula for a specific variable in general, so that we would do the algebraic steps only once, and then use the new formula to find the value of the specific variable. Now we will go through the steps of completing the square using the general form of a quadratic equation to solve a quadratic equation for x.

We start with the standard form of a quadratic equation and solve it for x by completing the square.

The solutions to a quadratic equation of the form ax2 + bx + c = 0, where are given by the formula:

To use the Quadratic Formula, we substitute the values of a, b, and c from the standard form into the expression on the right side of the formula. Then we simplify the expression. The result is the pair of solutions to the quadratic equation.

Notice the formula is an equation. Make sure you use both sides of the equation.

Solve by using the Quadratic Formula:

Solve by using the Quadratic Formula: .

Solve by using the Quadratic Formula: .

x = 3.

Standard Form Of Parabola Equation

The equation of parabola can be expressed in two different ways, such as the standard form and the vertex form. The standard form of parabola equation is expressed as follows:

f = y= ax2 + bx + c

The orientation of the parabola graph is determined using the a value.

• If the value of a is greater than 0 , then the parabola graph is oriented towards the upward direction.
• If the value of a is less than 0 , then the parabola graph opens downwards.

The axis of symmetry from the standard form of the parabola equation is given as x= -b/2a.

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Algebra 1 Unit 8 Test Quadratic Equations Answer Key

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Use The Discriminant To Predict The Number And Type Of Solutions Of A Quadratic Equation

When we solved the quadratic equations in the previous examples, sometimes we got two real solutions, one real solution, and sometimes two complex solutions. Is there a way to predict the number and type of solutions to a quadratic equation without actually solving the equation?

Yes, the expression under the radical of the Quadratic Formula makes it easy for us to determine the number and type of solutions. This expression is called the discriminant.

Lets look at the discriminant of the equations in some of the examples and the number and type of solutions to those quadratic equations.

2 real solutions 2 complex solutions 1 real solution

How To Graph Parabola

Two points define a line. Since parabola is a curve-shaped structure, we have to find more than two points here, to plot it. We need to determine at least five points as a medium to design a pleasing shape. In the beginning, we draw a parabola by plotting the points.

Suppose we have a quadratic equation of the form y=ax2+ bx + c, where x is the independent variable and y is the dependent variable. We have to choose some values for x and then find the corresponding y-values. Now, these values of x and y values will provide us with the points in the x-y plane to plot the required parabola. With the help of these points, we can sketch the graph.

In case, if the parabola equation is provided in the vertex form, first check the value of a. If the value of a is positive, then the parabola graph is upwards, otherwise, it is negative. Next, determine the vertex point from the given equation. Then, we have to substitute some value of x and find the corresponding values of y. Finally, plot all the values in the graph to obtain a parabola.

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Algebra I Unit 8 Test Quadratic Equations

Transcription

1 Name: Date: Per: Algebra I Unit 8 Test Quadratic Equations Find the axis of symmetry and vertex for the following equations. 1. y x 4x 1. 8 Axis of Symmetry Vertex Axis of Symmetry Vertex Complete each part using the given graph. 3. Axis of Sym: Domain: Vertex: Range: Zeros: Equation: A. x 3 C. B. x 3 D Axis of Sym: Vertex: Domain: Range: Zeros: Equation: A. y 9 C. B. y 9 D. 1 1 5. The graph of the function y = x is reflected across the x-axis, then translated two units left and six units down, write an equation to represent the new function. 6. If the graph of the function y = x is translated so its vertex is now at the point , which equation represents the new function? A. B. C. D. y y 3 3 Gina Wilson ,

2 7. Given the function, check all transformations that occurred from the graph of the function y = x. 1 x 4 3 up 7 units up 4 units vertical stretch down 7 units down 4 units vertical compression – left 7 units left 4 units – reflection in x-axis – right 7 units right 4 units – reflection in y-axis 8. Choosing from the binomial factors shown below, write the equation of the parabola shown to the left in factored form. Write your answers in the boxes. x + x x + 7 x 7 y = 9. Write the equation below in standard form, factored form, then identify the zeros. 5 Standard Form: Factored Form Zeros: 10. Select the equation that represent the parabola graphed below. y y 4 5 9 Gina Wilson ,

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The Practice Test Key Is Posted Below

Unit 8 -Quadratic Equations

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