Solving Quadratic Equations Review

Solving Quadratic Equations Review

Ms. Deveaux Precalculus 12

Quadratic Equation

A quadratic equation is any equation that can be rearranged in standard form as

 $ax^2+bx+c=0$  where a, b and c are numbers and  $a\ne0$ . 

Multiple Select

Which of the following are quadratic equations?

• $2x+5=7$
  

• $x^2+5x-24=0$

• $2x^2-5=11$

• $x^2+3y-4=0$

Solving Quadratic Equations

There are lots of different methods to find the roots of a quadratic equation. Here are a few:

-Trial and error

-Factoring

-Completing the square

-Quadratic formula

Multiple Choice

Solve this quadratic equation by factoring:

 $0=x^2+6x-16$  

•  $x=2,\ x=8$  

•  $x=-2,\ x=-8$  

•  $x=-2,\ x=8$  

•  $x=2,\ x=-8$  

Fill in the Blanks

One of the roots of this equation is 6. What is the other root?

 $x^2-x-30=0$  

Fill in the Blanks

What is one of Mrs. Deveaux's favourite bands?

Multiple Choice

What is the name of the vertical line that goes through the vertex of a parabola?

• The axis of evil

• Vertical line test

• The derivative

• The axis of symmetry

Quadratic Formula

The quadratic formula is a powerful tool for finding the roots of any quadratic equation.

Multiple Choice

Use the quadratic formula to find the roots of this equation:  $x^2+3x=5$  

•  $\frac{-3\pm\sqrt{29}}{2}$  

•  $\frac{3\pm\sqrt{29}}{2}$  

•  $\frac{-3\pm\sqrt{-11}}{2}$  

•  $\frac{3\pm\sqrt{-11}}{2}$  

Fill in the Blanks

This scene is from one of Mrs. Deveaux's favourite television show. What show is it?

The Discriminant

The discriminant is part of the quadratic formula. It tells you how many roots a quadratic equation has.

Fill in the Blanks

What is the value of the discriminant of this quadratic equation?  $2x^2-6x+3=0$  

Fill in the Blanks

Use the discriminant to determine the number of roots for this quadratic equation:  $x^2-6x+9=0$  

Open Ended

Mrs. Deveaux said that she hurt her foot when a trailer hitch fell on it... boring.

Create a more exciting story that Mrs. Deveaux could tell about how she injured her foot. Perhaps in a mosh pit at a rock concert or while mountain climbing...