Question

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

Answer 1

Answer:

twice

Step-by-step explanation:

Answer 2

Answer:

The function intersect the x-axis two times

Step-by-step 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

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

$x=\frac{-3(+/-)\sqrt{49}} {-4}$

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

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

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

so

The function has two x-intercepts

therefore

The function intersect the x-axis two times