Question 20

Standard Form of Quadratic Equations

Write each quadratic equation in standard form by moving all terms to the left side of

the equal sign. Identify coefficients a, b and c

Original Equation

Standard Form and Coefficients

-8x² + 3x = -4

x² - 10x = -5x +9

(x-7)(x − 3) = 10

-

3(x + 1)² + 6 = x

a=

a=

a=

a=

b=

b=

b=

b=

CU

C=

C=

C=/nGiven the function f(x) = x² - 8x + 12 find x when f(x)

8x + 12 find x when f(x) = 4 using your graphing calculator. Then

follow the steps below to show the solutions graph on the computer. [Hint: Use the following window on

your graphing calculator: Xmin=-5, Xmax = 12, Ymin=-9, Ymax = 9]

1. Write the solutions as a list of ordered pairs below. Round the values of a to two decimal places.

[Hint: If two solutions exist, enter them as (x1, y₁), (2, 32). If only one solution exists, enter

(x1, y1). If no solutions exist, enter DNEJ

2. Use the Line Tool to draw the Horizontal Line y = 4.

3. Use the Polynomial Tool to draw f(x) = x² - 8x + 12. [Hint: You will need to find the vertex

and one other point]

4. Use the Point Tool to identify the solutions.

Write the Points of Intersections as a list of Ordered Pairs

Draw the resulting graph and plot the points of intersection

94

8-

7+

6 +

1

-6

8 9 10 11 12/nSolving Quadratic Equations Graphically

2

Given the function f(x) = -x² + 10x - 12 find x when f(x) = 13 using your graphing calculator.

Then follow the steps below to show the intersection graph on the computer. [Hint: Use the following

window on your graphing calculator: Xmin=-5, Xmax = 10, Ymin=-5, Ymax = 18]

1. Write the points of intersection as a list of ordered pairs below. Round the values of a to two

decimal places.

[Hint: If two solutions exist, enter them as (x1, y₁), (x2, y2). If only one exists, enter (x1, y₁). If

none exist, enter DNE]

2. Use the Line Tool to draw the Horizontal Line y = 13.

3. Use the Polynomial Tool to draw f(x) = -x² + 10x - 12. [Hint: You will need to find the

vertex and one other point]

4. Use the Point Tool to identify the points of intersection.

Write the Points of Intersections as a list of Ordered Pairs

Draw the resulting graph and plot the points of intersection

1-3

17

16

15-

14

13

12

10

9.

T

2

5

S

9

10