# Exercises: Quadratic Functions & Parabola

## Exercise 1

For each of the parabola, listed further down, do each of the following:

1. State the value of the $$x^2$$ coefficient, $$a$$ and whether it is concave-up or concave-down.
2. State whether its vertex is a maximum or a minimum.
3. State the coordinates of its $$y$$-intercept.
The parabola are listed here:
1. $$y=3x^2-7x+1$$
2. $$y = -2x^2+3x - 5$$
3. $$y=-x^2+4x-8$$
4. $$y=x^2+5x-10$$
5. $$y = \frac{x^2}{2}-4x+5$$

## Exercise 2

Find the equation of the axis of symmetry of each of the following parabola:

1. $$y=x^2 - 2x - 6$$
2. $$y = -x^2+6x-4$$
3. $$y = 2x^2-20x+18$$
4. $$y=4x^2-4x+1$$
5. $$y=\frac{x^2}{2}+x+2$$

## Exercise 3

For each of the parabola, listed further down, do each of the following:

1. State whether it is concave-up or concave-down.
2. Find the coordinates of its vertex.
3. State its range.
The parabola are listed here:
1. $$y=2x^2-12x+10$$
2. $$y = -x^2-6x-5$$
3. $$y = -3x^2+6x$$
4. $$y=3x^2+12x+2$$
5. $$y=x^2-2x+1$$

## Exercise 4

For each of the following parabola find the coordinates of its $$x$$-intercepts:

1. $$y=x^2+x-6$$
2. $$y = -2x^2-4x+6$$
3. $$y = 7x^2-14x+7$$
4. $$y=4x^2+20x$$
5. $$y=-x^2-10x-25$$
6. $$y = 3x^2-9x-12$$
7. $$y = x^2+4x + 7$$
8. $$y = -9x^2+3x+2$$
9. $$y = -2x^2+2x-20$$
10. $$y = 8x^2+8x+2$$

## Exercise 5

For each of the parabola, listed below, do each of the following:

1. State the coordinates of the $$y$$-intercept.
2. Find the coordinates of the $$x$$-intercepts.
3. Find the equation of the axis of symmetry.
4. Find the coordinates of the vertex.
5. Sketch the parabola, labelling and "key points" and drawing the axis of symmetry.

The parabola are listed here:

1. $$y=2x^2-12x+10$$
2. $$y=-x^2+2x+8$$
3. $$y=3x^2+6x+3$$
4. $$y = x^2-8x+19$$
5. $$y = 2x^2+4x - 6$$