Find the x-intercept of a porabola with a vertex of (-3,-14) and y-intercept (0,-13)

see explanation

Step-by-step 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) = (- 3, - 14), thus

y = a(x + 3)² - 14

To find a substitute (0, - 13) into the equation

- 13 = 9a - 14 ( add 14 to both sides )

9a = 1 ( divide both sides by 9 )

a = , hence

y = (x + 3)² - 14 ← equation of parabola

To find the x- intercepts let y = 0

(x + 3)² - 14 = 0

Multiply through by 9

(x + 3)² - 126 = 0 ( add 126 to both sides )

(x + 3)² = 126 ( take the square root of both sides )

x + 3 = ± = ± 3

Subtract 3 from both sides

x = - 3 ± 3

The x- intercepts are therefore

x = - 3 - 3 ≈ - 14.22 ( to 2 dec. places ) or

x = - 3 + 3 ≈ 8.22 ( to 2 dec. places )

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

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step-by-step explanation: