Question

Which function describes this graph?

Answer 1

Answer:

C. y = x2 + 8x + 12

Step-by-step explanation:

To find x intercept/zero, substitute y = 0

0 = x^2 + 8x + 12

x^2 += 8x + 12 = 0

x^2 + 8x + 12 = 0

Solve the quadratic equation

• ax^2 + bx + c = 0 using x = -b±$\sqrt{b^2 -4ac$ / 2a
• x = -8±$\sqrt{8^2 -4(1)(12)$ / 2(1)

x = -8±$\sqrt{8^2 -4(12)$ / 2(1)

any expression multiplied by 1 remains the same

x= -8±$\sqrt{8^2 - 4(12)$ / 2(1)

Evaluate the power

8^2

write the exponentiation as a multiplication

8(8)

multiply the numbers

64

x = -8±$\sqrt{64 - 4(12)$ / 2(1)

multiply the numbers

x = -8±$\sqrt{64 - 48$ / 2(1)

any expression multiplied by q remains the same

x = -8±$\sqrt{64-48$ /2

subtract the numbers

x = -8±$\sqrt{16$ / 2

calculate the square root

x= -8± 4 / 2

x= -8 + 4 / 2

x= -8 - 4 / 2

simplify the expression

x = -2

x = -8 - 4 / 2

x = -2

x = -6

final solutions are

x1 = -6, x 2 = -2

Answer 2

Answer:

C.

y=x^2+8x+12