Question

For the function $f\left(x\right)=2x^2-7x+5$, find

(a) the zeros of the function

(b) any $x$-intercepts of the graph of the function

(c) any $y$-intercepts of the graph of the function.

Short answer

The zeroes, $x,y$intercept are$(1,\frac{5}{2}),(1,\frac{5}{2}),5$respectively

Step-by-step solution

Given information

Given the function$2x^2-7x+5$

Calculate the zeroes 

Substituting to zero, we get

$2x^2-7x+5=0$

$$\begin{gathered} 2x^2-5x-2x+5=0 \\ x(2x-5)-1(2x-5)=0 \\ (x-1)(2x-5)=0 \\ x=1,\frac{5}{2} \end{gathered}$$

Substitute x=0 for y intercept

Setting to zero, we get

$$\begin{gathered} y=2x^2-7x+5 \\ y=2{\left(0\right)}^2-7\left(0\right)+5 \\ y=5 \end{gathered}$$

Substitute y=0 for x intercept

Setting to zero, we get

$x=1,\frac{5}{2}$