Quadratic Relations

Unit 3: Standard form

Learning Goals

1. Complete the square to get vertex form

2. Solve for x using vertex form

3. Use quadratic formula t solve for x intercepts

Unit Summary

In this unit, we first learned to complete the square to get vertex form, and we next learned to solve for x using the vertex form. Then we learned how to use the quadratic formula to solve for x intercepts and finally learned to apply the quadratic formula for word problems.

Quadratic formula example

For the parabola y=4x^2+24x+41

1. Find x intercepts using quadratic formula

2. Find A.O.S


x= (-b +/- sqrt -b^2 - 4ac) ÷ 2a

x= (-24 +/- sqrt -24^2 -4(4)(41)) ÷ 2(4)

x= (-24 +/- sqrt -24^2 - 656) ÷ 8

x= (-24 +/- sqrt -576 - 656) ÷8

x= (-24 +/- sqrt 80) ÷ 8

x= (-24 +/- 8.94) ÷ 8

x= (-24 + 8.94) ÷ 8 and x= (-24-8.94) ÷ 8

x= -15.06 and x= -32.94


A.O.S = -15.06 - 32.94 ÷ 2

A.O.S= -24

Comletig the Square example

Rewrite in the form y=a(x-h)^2+k by completing the square


y= x^2 + 6x + 2

y= ( x^2 + 6x ) +2

y= ( x^2 + 6x + 9 - 9 ) + 2

y= ( x^2 + 6x + 9 ) - 7

y= ( x + 3 ) ^2 - 7

Word Problem Using Completing the Square

A wholesaler sells CDs for $8 each, and he presently sells 50 tomeach store. For every $0.50 decrease in his price, he will sell 5 more CDs.


a) write revenue equation

R= price x quantity

R= ( 8.00 - 0.50x )( 50 + 5x )


b) write equation to maximize revenue

400x + 40x - 25x - 2.5x^2

=400x + 15x - 2.5x^2

=( -2.5x^2 + 15x ) + 400

= -2.5( x^2 - 6x ) + 400

= -2.5( x^2 - 6x + 9 - 9 ) + 400

= -2.5(x^2 - 6x + 9 ) + 22.5 + 400

= -2.5(x - 3) ^2 + 422.5


c) solve revenue equation

r=(8.00 - 0.50 (3) )( 50 + 5(3))

r=(8.00 - 1.5)

r= 6.5