Question

Find the X intercept and coordinate of the vertex for the parabola Y=X^2+ 4X -21 ,if there is more than one Y intercept separate them with commas.

Answer 1

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:

$xv\text{ = }\frac{-b}{2a}=\frac{-4}{2\cdot1}=-2$$\begin{gathered} yv=xv^2+4xv\text{ -21} \\ yv=(-2)^2+4(-2)\text{ - 21 = - 25} \end{gathered}$

(xv , yv)

(- 2, -25)

The answer is:

x-intercepts:

(-7 , 0)

(3 , 0)

vertex:

(- 2, -25)