help!!!!!! i don't get this?

Question

Write each quadratic function in vertex form, if not already in it, identify the vertex, axis of symmetry and direction of opening?

y = -x^2 + 4

y = -5x^2 + 9

y = x^2 + 6x + 2

Answer 1

Vertex form is:
y = a(x - h)² + k

The first two equations are already in this form. In this form, x = h would be the axis of symmetry. So in case #1 and #2, the axis of symmetry is x = 0 (the y-axis).

The vertex is the point (h, k), so the first two are:
(0, 4) and (0, 9) respectively.

Finally, if a is a positive number, the parabola opens up. If it is negative, it opens down. In both your cases #1 and #2, the parabola opens down.

Now what about the third case? Since you have 6x in there, it is not in vertex form. You need to complete the square to get it into vertex form.

Start by moving the 2 to the left side:
y - 2 = x² + 6x

Now if there was a coefficient on the x² term you would divide both sides by that, but there isn't so you can skip that step.

Take the coefficient on the x term (6), take half (3) and square it (9). This is the number you need to add to both sides.
y - 2 + 9 = x² + 6x + 9
y + 7 = x² + 6x + 9

Write the right side as a perfect square:
y + 7 = (x + 3)²

Finally move the 7 back to the right and you have it in vertex form:
y = (x + 3)² - 7.

Comparing to:
y = a(x - h)² + k

a = 1
h = -3 (remember x + 3 = x - (-3))
k = -7

Now you can answer the questions.
The axis of symmetry is about the line y = -3
The vertex is (h, k) = (-3, -7)
Since a is positive, the parabola opens up.

Answer 2

Vertex form means there's no isolated x term: y = a(x-b)^2 + c. It's called this because you can read off the vertex as (b, c).

y = -x^2 + 4: already in vertex form. The vertex is (0, 4), the axis of symmetry is x = 0 and it opens downwards.

y = -5x^2 + 9: already in vertex form. The vertex is (0, 9), the axis of symmetry is x = 0 and it opens downwards.

y = x^2 + 6x + 2 = (x + 3)^2 - 3^2 + 2 = (x + 3)^2 - 7.
The vertex is (-3, -7), the axis of symmetry is x = -3 and it opens upwards.

Answer 3

1.y=-x^2+4
vertex=(0,-6)
axis of symmetry x=0
opening downward

2.vertex=(0,-9)
axis of symmetry x=0
opening downward

3.y=(x+3)^2-7
axis ofsymmetry x=-3
direction upwards
vertex (-3,7)

Answer 4

sorry know clue wont learn that till next year