Solve Quadratics

Find the value of c!!

Find the c-value that makes it a perfect square trinomial (quadratic)

#1.) x² +12x +c #2.) x² - 3x + c

To find c, take half of the b-value, then square that number!

#1.) 12/2 = 6^2 = 36

c = 36

#2.) -3/2 = (-3/2)^2 = 9/4

c=9/4

Multiple Choice

Find the value of c for the quadratic function:

$$f\left(x\right)=x^2+8x+c$$

Select the correct answer

• 8

• 4

• 16

• 20

​x²+6x = - 15

x² +6x + 9 = -15 + 9

(x + 3)² = - 6

(x + 3)² +6

x² -4x = -3

x² - 4x + 4 = - 3 + 4

(x - 2)² = 1

(x - 2)² - 1

Steps: Rewrite the quadratic in vertex form:

Move the end number to the right

Find the value of c (take half the value of b, then square that number

(add it on both sides of the equal sign)

Write the perfect square expression raised to the power of 2

Move the number on right back to the left, using the opposite sign

2x² +16x = 21

2(x²+8x + 16) = 21 + 32

2(x + 4)² = 53

2(x +4 )² - 53

Multiple Select

Rewrite the quadratic in vertex form:

$$f\left(x\right)=x^2+8x+12$$

$$f\left(x\right)=\left(x-h\right)^2\ +\ k\$$

(identify the h and k)

• h = -4

• h = 4

• k = 4

• k=-4

​​Solve by using square root!

Multiple Select

What are the solutions for the equation

$$\left(x+2\right)^2+49=0$$

Select all the correct answers.

• 2 - 7i

• -2 + 7i

• -2 - 7i

• 2 + 7i

Solve by completing the square

Multiple Select

Solve by completing the square:

$$x^2-x=4$$

Select all the correct answers

• $$\frac{1+\sqrt[]{17}}{2}$$

• $$\frac{1-\sqrt[]{17}}{4}$$

• $$\frac{1+\sqrt[]{17}}{4}$$

• $$\frac{1-\sqrt[]{17}}{2}$$