Question

Which function describes this graph?

—
10
А. y = (х – 4 )(х - 4)
В. у = х2 - 2x +6
оооо
ос. у = х2 + 8х +12
D. у = (х-2)(х – 6).

Answer 1

C. y = x2 + 8x + 12

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