# Math Help - sketching of Parabola graph

1. ## sketching of Parabola graph

how do I draw this? What method can I use?

Q: Plot the graph of y=3(x+2)squared -3 for the domain -5<x<2 and determine the following:
1.1 Turning point
1.2 Axis of symmetry
1.3 x-intercepts
1.4 y-intercepts
1.5 domain
1.6 Range

2. Originally Posted by Dreamer
how do I draw this? What method can I use?

Q: Plot the graph of y=3(x+2)squared -3 for the domain -5<x<2 and determine the following:
1.1 Turning point
1.2 Axis of symmetry
1.3 x-intercepts
1.4 y-intercepts
1.5 domain
1.6 Range
$P: y = 3(x+2)^2-3$ . With such a form of the equation of a parabola you can get all necessary values.

1.1 Turning point: V(-2, -3)
1.2 Axis of symmetry: x = -2. The parabola opens upward (3>0) and is stretched(?) by the factor 3.
1.3 x-intercepts: $y = 0~\implies~(x+2)^2=1~\implies~x=-3~\vee~x=-1$
1.4 y-intercepts: $x = 0~\implies~y=9~\implies~Y(0,9)$
1.5 domain: given: $-5 < x < 2$
1.6 Range: $min_p = -3$ see coordinates of vertex.
$p(-5) = 24$, $p(2) = 45$. Therefore $max_p = p(2)
$

Therefore the range is r = (-3;45)