Question

You dont have to answer both of 3 and 4 you can answer one if you'd like.

Answer 1

below

Explanation:

3. 2x² - 2x + 9 = y

a) The equation of the axis of symmetry is x = 0.5 (since it's the x-coordinate of the vertex)

b) To find the vertex, we need to complete the square:

2x² - 2x + 9 = y

2(x² - x) + 9 = y

2(x² - x + 1/4) + 9 - 2(1/4) = y

2(x - 1/2)² + 8.5 = y

So the vertex is at (0.5, 8.5).

c) The parabola opens up since the coefficient of x² is positive.

d) The vertex is the minimum point.

4. -x² + 10x = y

a) The equation of the axis of symmetry is x = 5 (since it's the x-coordinate of the vertex).

b) To find the vertex, we need to complete the square:

-x² + 10x = y

-(x² - 10x) = y

-(x² - 10x + 25 - 25) = y

-(x - 5)² + 25 = y

So the vertex is at (5, 25).

c) The parabola opens down since the coefficient of x² is negative.

d) The vertex is the maximum point.