Q 6.101 - Intermediate Algebra

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.

Step-by-Step Solution

Answer

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

Step 1: Given information

Given the function $2x^2-7x+5$

Step 2: Calculate the zeroes

Substituting to zero, we get

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

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

Step 3: Substitute x = 0 for y intercept

Setting to zero, we get

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

Step 4: Substitute y = 0 for x intercept

Setting to zero, we get

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