Question

What are the x- and y-intercepts of the graph of y = x2 + 3x − 10? x-intercepts: (−2, 0) and (5, 0) y-intercept: (0, 10) x-intercepts: (−2, 0) and (−5, 0) y-intercept: (0, 10) x-intercepts: (−2, 0) and (5, 0) y-intercept: (0, −10) x-intercepts: (2, 0) and (−5, 0) y-intercept: (0, −10)

Answer 1

We have the following function:

$f(x)=x^2+3x-10$

So, we need to find the x- and y-intercepts of the graph of that function, therefore:

1. x-intercepts

x-intercepts can be found when $y=0$, so:

$0=x^2+3x-10 \\ \\ Using \ Quadratic \ Formula \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ Where: \\ \\ a=1, b=3, c=-10 \\ \\ x=\frac{-3 \pm \sqrt{3^2-4(1)(-10)}}{2(1)} \\ \\ Two \ values: \\ \\ x=2 \ and \ x=-5$

So, the x-intercepts are:

$\boxed{(2,0) \ and \ (-5, 0)}$

2. y-intercepts

x-intercepts can be found when $x=0$, so:

$y=(0)^2+3(0)-10 \\ \\ \therefore y=-10$

So, the y-intercept is:

$\boxed{(0,-10)}$

_______________________________________

Therefore the right answer is:

x-intercepts: (2, 0) and (−5, 0) y-intercept: (0, −10)

This is indicated in the Figure bellow.