Question

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

Answer 1

Answer:

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

Answer 2

The formula of the quadratic function is $y = -8x^2 + 6$

A quadratic function is represented as:

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

The vertex of the quadratic function is given as:

$(h,k) = (0,6)$

So, we have:

$y = a(x - 0)^2 + 6$

This gives:

$y = ax^2 + 6$

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

So, we have:

$-2 = a(-1)^2 + 6$

$-2 = a + 6$

Subtract 6 from both sides

$a = -8$

Substitute -8 for a in $y = ax^2 + 6$

$y = -8x^2 + 6$

Hence, the formula of the quadratic function is $y = -8x^2 + 6$

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