The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12). Which quadratic function represents the parabola in standard form?

Solution:

Given, the vertex of a parabola is (-2, -20) and its y-intercept is (0, -12).

We have to find the quadratic equation that represents the parabola in standard form.

The equation of the parabola in vertex form is given by

y = a(x - h)² + k

Where, (h, k) is the vertex.

Given, (h, k) = (-2, -20)

y = -12

-12 = a(0 - (-2))² + (-20)

-12 = a(2)² - 20

4a - 20 = - 12

4a = -12 + 20

4a = 8

a = 8/4

a = 2

Now, y = 2(x - (-2))² + (-20)

y = 2(x + 2)² - 20

y = 2(x² + 2x + 4) - 20

y = 2x² + 4x + 8 - 20

y = 2x² + 4x - 12

Therefore, the required quadratic function is y = 2x² + 4x - 12.

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The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12). Which quadratic function represents the parabola in standard form?

Summary:

The vertex of a parabola is (-2, -20), and its y-intercept is (0, -12). The quadratic function y = 2x² + 4x - 12 represents the parabola in standard form.