Question

Sketch the graph of the equation Y=2x^2-10x+9

Answer 1

Solution:

The equation is given below as

$y=2x^2-10x+9$

Step 1:

We will figure out the y-intercept by putting x=0

$\begin{gathered} y=2x^{2}-10x+9 \\ y=2(0)^2-10(0)+9 \\ y=9 \\ (0,9) \end{gathered}$

Step 2:

Calculate the vertex of the graph using the formula below

$\begin{gathered} y=2x^2-10x+9 \\ x=-\frac{b}{2a},b=-10,a=2,c=9 \\ x=\frac{-(-10)}{2(2)}=\frac{10}{4}=\frac{5}{2} \\ \\ y=2(\frac{5}{2})^2-10(\frac{5}{2})+9 \\ y=2(\frac{25}{4})-25+9 \\ y=\frac{25}{2}-16 \\ y\frac{=25-32}{2} \\ y=-\frac{7}{2} \end{gathered}$

Hence,

The vertex of the equation is

$(\frac{5}{2},-\frac{7}{2})$

Using a graphing calculator, we will have the graph be