Contains (1, −6) has the shape of f(x) = 3x2 . Vertex has x-coordinate of −1. For the following exercises, write the equation of the quadratic function that contains..

For the following exercises, write the equation of the quadratic function that contains the given point and has the same shape as the given function.

Contains (1, −6) has the shape of f(x) = 3x2 . Vertex has x-coordinate of −1.

Solutions

Expert Solution

Consider the information provided in the problem.

The x-coordinate of vertex (h, k) is –1,

Therefore, h = -1,

The required graph has same shape as f(x) = 3x2,

Therefore, a = 3,

Consider the following,

x = 1,

f(x) = -6

Substitute all these in the standard form of quadratic equation.

f(x) = a(x – h)2 + k

-6 = 3{1 – (-1)}2 + k

-6 = 12 + k

k = -18

Now, substitute the values of a, h and k in quadratic equation.

f(x) = 3{x – (-1)}2 + (-18)

f(x) = 3x2 + 6x + 3 – 18

= 3x2 + 6x - 15

Hence, the required equation is f(x) = 3x2 + 6x - 15.

Hafiz answered 1 year ago

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