How many times does the graph of the function below intersect or touch the x-axis y=-2x^2+3x+5

Question

asked Sep 10, 2020 147k views

2 Answers

Amgando · Answer 1 · 2020-09-16T01:01:57+0000

Answer:

The function intersect the x-axis two times

Explanation:

we have

y=-2x^(2)+3x+5

To find the x-intercepts equate the equation to zero

so

0=-2x^(2)+3x+5

-2x^(2)+3x+5=0

The formula to solve a quadratic equation of the form
ax^(2) +bx+c=0 is equal to

$x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}$

in this problem we have

-2x^(2)+3x+5=0

so

$a=-2\\b=3\\c=5$

substitute in the formula

$x=\frac{-3(+/-)\sqrt{3^(2)-4(-2)(5)}} {2(-2)}$

$x=\frac{-3(+/-)√(49)} {-4}$

$x=\frac{-3(+/-)7} {-4}$

$x1=\frac{-3(+)7} {-4}=-1$

$x2=\frac{-3(-)7} {-4}=2.5$

so

The function has two x-intercepts

therefore

The function intersect the x-axis two times