Write a formula for quadratic function if its graph has the vertex at point (0,6) and passes through the point (−1,−2).

The formula of the quadratic function is

A quadratic function is represented as:

The vertex of the quadratic function is given as:

So, we have:

This gives:

The quadratic function passes through (-1,-2).

So, we have:

Subtract 6 from both sides

Substitute -8 for a in

Hence, the formula of the quadratic function is

Read more about quadratic functions at:

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y = - 8x² + 6

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (0, 6), thus

y = a(x - 0)² + 6, that is

y = ax² + 6

To find a substitute (- 1, - 2) into the equation

- 2 = a(- 1)² + 6, that is

- 2 = a + 6 ( subtract 6 from both sides )

- 8 = a

y = - 8x² + 6

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step-by-step explanation:

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)