Question

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

Answer 1

twice

Explanation:

Answer 2

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