helpppp! i cant understand this

Question

complete the table of values for the quadratic function y=2(x - 3 )^2 - 5. make sure include vertwx and 2  points on each side of the vertwx. draw and accurate graph of this quadratic function then answer the following:

a.  what are the coordinates of the vertex. label the vertex in graph

b. what is the equation of the axis of symmetry? draw and label the axis of symmetry on graph using dotted line

c. label the x-intercepts on graph

d. label the y intercepts on graph and show how to find the coordinates of the y intercepts methematically.

Answer 1

The quadratic equation is y = 2(x - 3)^2 - 5.

Compare the equation y = 2(x - 3)^2 - 5 with standard form of parabola equation y = a(x - h)^2 + k.

a = 2, h = 3 and k = -5.

Vertex = (h, k) = (3, - 5).

Axis of symmetry : x = h = 3.

To find x-intercept, substitute y = 0 in the original function y = 2(x - 3)^2 - 5.

0 = 2(x - 3)^2 - 5

2(x - 3)^2 - 5 = 0

(x - 3)^2 = 5/2

x = 3 ± √(5/2).

To find y-intercept, substitute x = 0 in the original function y = 2(x - 3)^2 - 5.

y = 2(0 - 3)^2 - 5

y = 13.

Make the table :

x	y = 2(x - 3)^2 - 5	y	(x, y)
1	y = 2(1 - 3)^2 – 5 = 3	3	(1, 3)
2	y = 2(2 - 3)^2 – 5 = -3	-3	(2, -3)
4	y = 2(4 - 3)^2 – 5 = -3	-3	(4, -3)
5	y = 2(5 - 3)^2 – 5 = 3	3	(5, 3)
6	y = 2(6 - 3)^2 – 5 = 13	13	(6, 13)

Graph :