Question

2- Answer the following question:

a. What are the four different ways to solve a quadratic function? (5 points)
b. Solvex² - 4x - 11 = 0 using completing the square. You must show all the steps. (10 points)
c. Solve 2x² + 16x + 24 = 0 using the quadratic formula. You must show all the steps. (10 points)

Answer 1

A. Four ways to solve a quadratic equation

---Factoring

---Completing the square

---Quadratic equation

---Graphing

B. Solve the equation by completing the square

x^2 - 4x - 11 = 0

x^2 - 4x = 11

x^2 - 4x + 4 = 11 + 4

(x - 2)^2 = 15

x - 2 = +/- 15

x - 2 = 15 || x = 17

x - 2 = -15 || x = -13

C. Solve the equation using the quadratic formula

Quadratic formula =
`(-b +/-√(b^2 - 4ac) )/(2a)`

Equation = 2x^2 + 16x + 24 = 0

a = 2

b = 16

c = 24

`(-16 +/- √(16^2 - 4(2)(24)) )/(2(2))`

`(-16 +/- √(256 - 192) )/(4)`

`(-16 +/- √(64) )/(4)`

`(-16 +/- 8 )/(4)`

[-16 + 8] / 4 = -2

[-16 - 8] / 4 = -6

x = -6, -2

Hope this helps!