Question

Draw the graph of
(
P(x) = (x+2) (x+3)​

Answer 1

Answer:

To find the vertex of curve

$p(x) \: = (x + 2)(x + 3) \\ = {x}^{2} + 2x + 3x + 6 \\ = {x}^{2} + 5x + 6 \\ p'(x) = 2x + 5 \\ put \: p'(x) = 0 \\ 2x + 5 = 0 \\ x = - \frac{5}{2} \\ so \: p( - \frac{5}{2} ) = ( - \frac{5}{2} + 2)( - \frac{5}{2} + 3) \\ = - \frac{1}{2} \times \frac{1}{2} \\ = - \frac{1}{4}$

So vertex of parabola = (-5/2, -1/4)

Point of intersection with x axis,

put p(x) = 0

(x + 2)(x + 3) = 0

x = -2 or x = - 3

point of intersection with x axis is (-2, 0) and (- 3, 0).