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:

 $0=x^2+6x-16$  

•  $x=2,\ x=8$  

•  $x=-2,\ x=-8$  

•  $x=-2,\ x=8$  

•  $x=2,\ x=-8$  

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:  $x^2+3x=5$  

•  $\frac{-3\pm\sqrt{29}}{2}$  

•  $\frac{3\pm\sqrt{29}}{2}$  

•  $\frac{-3\pm\sqrt{-11}}{2}$  

•  $\frac{3\pm\sqrt{-11}}{2}$  

The Discriminant

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

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...