Question

Look at picture
Write the equation in vertex form and standard form.​

Answer 1

see explanation

Explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (- 2, 2), thus

y = a(x + 2)² + 2

To find a substitute the point on the graph (0, 0) into the equation

0 = a(0 + 2)² + 2

0 = 4a + 2 ( subtract 2 from both sides )

- 2 = 4a ( divide both sides by 4 )

-
`(1)/(2)` = a

y = -
`(1)/(2)`(x + 2)² + 2 ← in vertex form

Expanding and simplifying gives

y = -
`(1)/(2)`(x² + 4x + 4) + 2

= -
`(1)/(2)`x² - 2x - 2 + 2

= -
`(1)/(2)`x² - 2x ← in standard form