Question

Write an equation of a parabola in vertex form. Vertex (2,-3) and passes through (0,5)​

Answer 1

The parabola equation in vertex form passes through (0,5)​ is $y=2(x-2)^{2}-3$

Solution:

Given that, vertex of a parabola is (2,-3) and the parabola passes through the point (0, 5)

We have to find the equation of parabola in vertex form.

The general form of parabola equation in vertex form is given as:

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

Where (h, k ) is vertex and "a" is a constant

Here in our problem, h = 2 and k = - 3

By substituting the values in general form we get,

$\begin{array}{l}{y=a(x-2)^{2}+(-3)} \\\\ {\rightarrow y=a(x-2)^{2}-3}\end{array}$

Now, we know that it passes through (0, 5). So substitute x = 0 and y = 5

$\begin{array}{l}{\rightarrow 5=a(0-2)^{2}-3} \\\\ {\rightarrow a(-2)^{2}=5+3} \\\\ {\rightarrow 4 a=8} \\\\ {\rightarrow a=2}\end{array}$

So substituting the value of "a" we get,

$y=2(x-2)^{2}-3$

Hence, the parabola equation in vertex form is $y=2(x-2)^{2}-3$