Question

Write the equation of the quadratic function that contains the given point and has the same stretch factor as the given function.
Contains (1, −3) and has the same stretch factor as
f(x) = 3x2.
Vertex has x-coordinate of −1.

Answer 1

The quadratic function is y = 3x² + 6x - 12

Since a quadratic function is a parabola, we use the equation of a parabola in standard form.

y = a(x - h)² + k where a = stretch factor, h = x-coordinate of vertex and k = y-coordinate of vertex.

We are given that the quadratic function contains the point (1, -3) and has vertex x-coordinate at x = -1. That is h = -1.

Also, it has the same stretch factor as f(x) = 3x². So, a = 3

Thus, y = a(x - h)² + k

y = 3(x - (-1))² + k

y = 3(x + 1)² + k

Now, since the quadratic function passes through the point (1, -3), we have that

y = 3(x + 1)² + k

-3 = 3(1 + 1)² + k

-3 = 3(2)² + k

-3 = 3(4) + k

-3 = 12 + k

k = -3 - 12

k = -15

So,

y = 3(x + 1)² + k

y = 3(x + 1)² - 15

y = 3(x² + 2x + 1) - 15

y = 3x² + 6x + 3 - 15

y = 3x² + 6x - 12

So, the quadratic function is y = 3x² + 6x - 12

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