Question

Select the correct answer.

Which function does this graph represent?

A downward open parabola rises from (negative 2 point 4, negative 4) to (negative 1, 2) and declines through (0 point 4, negative 4) on the x y coordinate plane.

A.
f(x) = 3(x + 1)2 + 2
B.
f(x) = -3(x + 1)2 + 2
C.
f(x) = -3(x + 1)2 − 2
D.
f(x) = 3(x − 1)2 + 2

Answer 1

The parabola represented by this graph has the following equation:

y = -16.67(x + 1)² + 2

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

A downward open parabola rises from (-2.4, 4) to (-1,2), and declines through (0.4, -4) on the coordinate plane, hence the vertex is given by:

(-1,2), hence the coefficients are h = -1 and k = 2, and the equation is:

y = a(x - h)² + k

y = a(x + 1)² + 2

We have that when x = -0.4, y = -4, hence the leading coefficient is found as follows:

y = a(x + 1)² + 2

-4 = a(-0.4 + 1)² + 2

a = -6/0.6²

a = -16.67

Hence the equation is:

y = -16.67(x + 1)² + 2

More can be learned about the equation of a parabola at https://brainly.com/question/24737967

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