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PLEASE HELP AND ANSWER CORRECTLY

I know the axis of symmetry but I don't know how to put it in an equation

please review the graph and answer you may use the other answers to help

PLEASE HELP AND ANSWER CORRECTLY I know the axis of symmetry but I don't know how-example-1
PLEASE HELP AND ANSWER CORRECTLY I know the axis of symmetry but I don't know how-example-1
PLEASE HELP AND ANSWER CORRECTLY I know the axis of symmetry but I don't know how-example-2

1 Answer

8 votes

Answer:

standard form: y = x² - 2x - 8

vertex form: y = (x − 1)² - 9

factorized form: y = (x + 2)(x - 4)

Explanation:

From inspection of the graph:

  • Axis of symmetry: x = 1
  • Vertex = (1, -9)
  • x-intercepts = (-2, 0) and (4, 0)
  • y-intercept = (0, -8)

Standard quadratic form: y = ax² + b x + c

Vertex form of a quadratic equation: y = a(x − h)² + k

If a > 0 then the parabola opens upwards

If a < 0 then the parabola opens downwards

(h, k) is the vertex

c is the y-intercept

Inputting the vertex into the vertex form gives:

y = a(x − 1)² - 9

= a(x² - 2x + 1) - 9

= ax² - 2ax - 8

Using the x-intercepts to create a quadratic equation:

y = a(x + 2)(x - 4)

= a(x² - 2x - 8)

= ax² - 2ax - 8a

Comparing the y-intercepts:

-8 = -8a ⇒ a = 1

Therefore, y = x² - 2x - 8

User Thomas Auinger
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