Question

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

The equation of the parabola is
y= _________

Answer 1

The equation of the parabola is y = 2(x + 2)² - 20.

Use the vertex form of a quadratic function:

y = a(x - h)² + k, where (h, k) is the vertex of the parabola and a is a constant

Given the vertex (-2, -20), we substitute h = - 2 and k = - 20 into the vertex form to get:

y = a(x + 2)² - 20

To determine the value of a, we use the y-intercept (0, -12).

Substitute x = 0 and y = -12 into the equation to get:

-12 = a(0 + 2)² - 20

-12 = 4a - 20

4a = 8

a = 2

Therefore, the equation of the parabola is y = 2(x + 2)² - 20.

Answer 2

y = 2(x + 2)² - 20

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Use the vertex form of a quadratic function:

• y = a(x - h)² + k, where (h, k) is the vertex of the parabola and a is a constant

Given the vertex (-2, -20), we substitute h = - 2 and k = - 20 into the vertex form to get:

• y = a(x + 2)² - 20

To determine the value of a, we use the y-intercept (0, -12).

Substitute x = 0 and y = -12 into the equation to get:

• -12 = a(0 + 2)² - 20
• -12 = 4a - 20
• 4a = 8
• a = 2

Therefore, the equation of the parabola is y = 2(x + 2)² - 20.