Question

Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)

Vertex:
(−2, −12)
Point:
(0, −4)

Answer 1

The equation can be written as y = -2x^2 - 4x - 12.

Answer 2

Answer: 2x^2 + 8x - 4.

Explanation:

To write the standard form of a quadratic function, we use the vertex form, which is given by:

y = a(x - h)^2 + k

Where (h,k) is the vertex of the parabola, and "a" is the coefficient that determines whether the parabola opens upward or downward.

Using the vertex and the point that the parabola passes through, we can substitute these values to find the value of "a":

Vertex: (-2, -12)

Point: (0, -4)

Substituting these values into the vertex form, we get:

-4 = a(0 - (-2))^2 - 12

-4 = a(2)^2 - 12

-4 + 12 = 4a

8 = 4a

a = 2

Now that we have found the value of "a", we can write the quadratic function in standard form:

y = 2(x - (-2))^2 - 12

Simplifying this equation, we get:

y = 2(x + 2)^2 - 12

Expanding the squared term, we get:

y = 2(x^2 + 4x + 4) - 12

Multiplying through by 2, we get:

y = 2x^2 + 8x - 4

Therefore, the standard form of the quadratic function is:

2x^2 + 8x - 4.