In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
y = x² + 4x - 21
Step 02:
parabola equation:
y = x² + 4x - 21
a = 1
b = 4
c = -21
x-intercepts:
x² + 4x - 21 = 0
(x + 7)(x - 3) = 0
x1 = - 7
x2 = 3
(-7 , 0)
(3 , 0)
vertex:
[tex]xv\text{ = }\frac{-b}{2a}=\frac{-4}{2\cdot1}=-2[/tex][tex]\begin{gathered} yv=xv^2+4xv\text{ -21} \\ yv=(-2)^2+4(-2)\text{ - 21 = - 25} \end{gathered}[/tex](xv , yv)
(- 2, -25)
The answer is:
x-intercepts:
(-7 , 0)
(3 , 0)
vertex:
(- 2, -25)