Question

Use the equation to answer ALL of the questions below.

f(x) = 2x² + 8x - 4
What is the axis of symmetry? You can use the equation
What is the vertex of the parabola (x, y)?
What is the y-intercept of the parabola?

Answer 1

see explanation

Explanation:

given a parabola in standard form

f(x) = ax² + bx + c ( a ≠ 0 )

then the equation of the axis of symmetry is

x = -
`(b)/(2a)`

f(x) = 2x² + 8x - 4 ← is in standard form

with a = 2, b = 8 , then equation of axis of symmetry is

x = -
`(8)/(2(2))` = -
`(8)/(4)` = - 2

that is equation of axis of symmetry is x = - 2

the axis of symmetry passes through the vertex of the parabola

substitute x = - 2 into f(x) for corresponding y- coordinate

f(- 2) = 2(- 2)² + 8(- 2) - 4 = 2(4) - 16 - 4 = 8 - 20 = - 12

vertex = (- 2, - 12 )

the y- intercept is on the y- axis, where the x- coordinate is zero

substitute x = 0 into f(x)

f(0) = 2(0)² + 8(0) - 4 = 0 + 0 - 4 = - 4

y- intercept = - 4