Question

Where does the graph of y = 2x^2 + x − 15 cross the x-axis?

Answer 1

Cutting the `x` axis means `y=0`
Which means `2x²+x-15=0`

We are going to seek the `Delta` :
The equation is of the form `ax²+bx+c=0`
`a=2` ; `b=1` ; `c=-15`

`Delta=b²-4ac`
`Delta=1²-4*2*(-15)`
`Delta=1+120`
`Delta=121` ( `=sqrt11` )

`x_1=(-b-sqrtDelta)/(2a)`

`x_1=(-1-11)/4`

`x_1=-12/4`

`x_1=-3`

`x_2=(-b+sqrtDelta)/(2a)`

`x_2=(-1+11)/4`

`x_2=10/4`

`x_2=5/2`

Thus, the function cuts the `x` axis in `x=-3` and `x=5/2`

graph{2x^2+x-15 [-10, 10, -5, 5]}

Answer 2

`y = 2x^2+x-15 = (2x-5)(x+3)`

`y=0` when `x = 5/2` or `x=-3`

so the graph crosses the x-axis at `(-3, 0)` and `(5/2, 0)`