Question

Find the x-intercepts for the parabola defined by the equation below.

y = x2 + 9x + 14

Answer 1

To find the x-intercepts we solve the equation y=0.
We have :
\[y=0\iff x^2+9x+14=0\]
So :
\[\Delta=9^2-4\times14=25>0\]
So, there is two solutions :
\[x_1=\frac{-9+\sqrt{25}}{2}=\frac{-9+5}{2}=-2\\
x_2=\frac{-9-\sqrt{25}}{2}=\frac{-9-5}{2}=-7
\]
Therefore : the x-intercepts of the graph are (-2,0) and (-7,0).

Answer 2

The x-intercepts are the points where y=0.
Set y=0 and solve for x:
x^2 + 9x + 14 = 0
This can be factored as
(x+7)(x+2) = 0
So the x-intercepts are x=-2 and x=-7

Answer 3

thank you noura 11 !!!