Chapter 9 Test Review

Chapter 9 Test Review

Solving with Square Roots

• To cancel out a square root remember to square

• Exponent of 2

• Solve for x

Multiple Choice

 $3\sqrt{-9x+7}=-12$  Solve for the only possible solution.

• x = -5

• x = 5

• x = 3

• x = -1

Multiple Choice

 $3\sqrt{-9x+7}=-12$  Does your previous solution satisfy the equation?

• Yes

• No

Solving with Squares

• When working with squares, cancel with square root

• Remember that a square root will generate two roots

Multiple Select

Find all real solution of the following equation. Select all that apply.

 $\left(x-4\right)^2-25=0$  

• x = 9

• x = 13

• x = -1

• x = -5

Quadratic Formula

• Standard Form

•  $y=ax^2+bx+c$  

• Find a,b, and c terms

• Substitute into Quadratic Formula

•  $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  

Multiple Select

Use the Quadratic Formula to solve the following equation.

 $x^2-5x-4=0$  

•  $x=\frac{5+\sqrt{41}}{2}$  

•  $x=\frac{5-\sqrt{41}}{2}$  

•  $x=\frac{5-\sqrt{9}}{2}$  

•  $x=\frac{5+\sqrt{9}}{2}$  

Writing Equations

• 3 parts

• Roots

• Factors (from roots)

• Multiplicity (Exponent)

• Factors are written opposite of roots!

• Example: If roots are -6, 5, -10, 4 write as....

• (x + 6), (x - 5), (x + 10), (x - 4)

Multiple Select

Write a quadratic polynomial which has zeros at 9 and -4

• (x - 9)

• (x - 4)

• (x + 9)

• (x + 4)

Multiple Choice

Write a double root at -8

• $2\left(x-8\right)$

• $\left(x+8\right)^2$

• $2\left(x+8\right)$

• $\left(x-8\right)^2$

Key Features

• Vertex (Max/MIn)

• (x, y) x (axis of symmetry) y (value)

• Axis of Symmetry x =

• x-intercepts, solutions, roots, zeros

• y-intercept

Multiple Choice

Determine the vertex of the function below.

• (-7, 0)

• (-1, 0)

• (0, 7)

• (-4, -9)

Multiple Choice

Is it a max or a min? And what is the max/min value?

• Min: -4

• Min: -9

• Max: -4

• Max: -9