Question

Which quadratic function has Vertex (-1,4) and passes through (4,19) HELP

Answer 1

Answer:

$f(x)=\frac{3}{5}(x+1)^2+4$

Step-by-step explanation:

The equation of a quadratic function in vertex form is given by:

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

Where (h,k) is the vertex.

It was given in the question that the vertex of the parabola is (-1,4).

When we substitute the vertex into the formula we get:

$f(x)=a(x+1)^2+4$

The parabola also passes through (4,19) hence it must satisfy its equation.

$19=a(4+1)^2+4$

$19-4=a(5)^2$

$15=25a$

We divide both sides by 25 to get:

$a=\frac{15}{25}= \frac{3}{5}$

Hence the quadratic function is:

$f(x)=\frac{3}{5}(x+1)^2+4$