Solving Quadratics

Evaluate Equations

100

Given f(x)=-x², find f(-3)

f(-3)=-9

200

Given f(x)= -x²+17 find f(-3)

f(-3)=8

300

Given f(x)= -x² +2x, find f(-9)

f(-9)=-99

400

Given f(x)=-x²-3x+20 find f(6)

f(6)=-34

500

Given f(x)=4x²+3x-5, find f(-3.5)

f(-3.5)=-64.5

Factor to Standard Form

100

Rewrite the equation in standard form:

3x²+4=4x²-8x

x²-8x-4=0

200

Rewrite in standard form:

x²-6x+4=-4x²+7

5x²-6x-3=0

300

Convert to standard form: -6(x+8)(x+1)=0

−6x²−54x−48=0

400

Rewrite in standard form:

5x²+4x+13=12x²+8

7x²-4x-5=0

500

Convert to standard form:

-4(x-4)²+7=0

-4x²+32x-57=0

Quadratic Functions

100

y=x²+6

36

200

Determine the y value if x is 9

y=x²-4x+19

y=64

300

Solve the equation for all real solutions, in simplest form:

4q²−15q+12=0

q=815±33^1/2/8

400

Find the y intercept:

0=-2x²+3x+2

(0,2)

500

Find the vertex:

-(x+8)²+5=0

(-8,5)

Factored Equations

100

Solve the equation for all values of x.

−3(x+4)(x²−9)=0

x=−4, x=3, x=−3

200

Solve the equation for all values of x.

−3x(10x+3)(x²+16)=0

x=0, x=−103, x=4i, x=−4i

300

Solve the equation for all values of x.

−x(x²−1)(49x²−16)=0

x=0, x=1, x=−1, x=74, x=−74

400

Solve the equation for all values of x.

2(7x−6)(x²+25)=0

x=76, x=5i, x=−5i

500

Solve the equation for all values of x.

(x²−100)(100x²−81)=0

x=10, x=−10, x=109, x=−109

Discriminant

100

Find the discriminant:

x²-9x+4=0

65

200

Find the discriminant:

3x+14=2x²

103

300

Find the discriminant:

3(x-3)²+6=0

-72

400

Find the discriminant:

2(x-5)(x+6)=0

484

500

Find the discriminant:

4x-2=-3x²+5x

25