Question

Write the equation of the quadratic function vertex
form that has vertex (2, −3) and passes through the
point (1, 4).

Answer 1

Given that the vertex of the quadratic function is (2,-3) and passes through the point (1,4)

We need to determine the equation of the quadratic function.

Equation of the quadratic function:

The vertex form of the quadratic function is given by

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

where the vertex is (h,k) and a is a constant.

Substituting the vertex (2,-3) in the vertex form of the quadratic function, we get;

$y=a(x-2)^2-3$ -------(1)

Since, it passes through the point (1,4), let us substitute the points (1,4) in the above formula, we get;

$4=a(1-2)^2-3$

$4=a(-1)^2-3$

$4=a-3$

$7=a$

Thus, the value of the constant a is 7.

Substituting $a=7$ in equation (1), we get;

$y=7(x-2)^2-3$

$y=7(x^2-4x+4)-3$

$y=7x^2-28x+28-3$

$y=7x^2-28x+25$

Thus, the equation of the quadratic function is $y=7x^2-28x+25$