Question

Find the vertex and write the quadratic function in vertex form.f(x)=x^2−6x+25

Answer 1

A quadratic equation in its standard formula y = ax² + bx + c, can also be written in the vertex form: y = a(x - h)² + k where the point (h, k) is the vertex of the parabola.

Then, to solve this question, follow the steps below.

Step 01: Find x-vertex.

The x-vertex (h) can be found using the equation:

$h=\frac{-b}{2a}$

In this equation,

b = -6

a = 1

Then,

$\begin{gathered} h=-\frac{(-6)}{2\cdot1} \\ h=\frac{6}{2} \\ h=3 \end{gathered}$

Step 02: Substitute x by 3 in the standard form to find y-vertex (k):

$\begin{gathered} y=x^2-6x+25 \\ y=3^2-6\cdot3+25 \\ y=9-18+25 \\ y=-9+25 \\ y=16 \end{gathered}$

So, k = 16.

Step 03: Substitute the values in the vertex form.

a = 1

h = 3

k = 16

$\begin{gathered} y=a\cdot(x-h)^2+k \\ y=1\cdot(x-3)^2+16 \\ y=(x-3)^2+16 \end{gathered}$

Answer:

$y=(x-3)^2+16$