Calculate points from this table and plot the points as you go. x y The basic parabola is shown on the graph, dotted blue. Draw a parabola through the points. Adding 2 to x2 moves the basic parabola up by 2 units. How?

x y Calculate points from this table and plot. The basic parabola is shown on the graph, dotted blue. Draw a parabola through the points. Subtracting 3 from x2 moves the basic parabola down by 3 units. How?

x y Calculate points from this table and plot. The basic parabola is shown on the graph, dotted blue. Draw a parabola through the points. Adding 4 to x and then squaring moves the basic parabola How? to the left by 4 units.

x y Calculate points from this table and plot. Draw a parabola through the points. The basic parabola is shown on the graph, dotted blue. Subtracting 1 from x and then squaring moves the basic parabola How? to the right by 1 unit.

y parabola the moves 2 The - 2 units to the right. How? x

y parabola the moves 3 The - 3 units down. How? x

x y Calculate points from this table and plot. The basic parabola is shown on the graph, dotted blue. Draw a parabola through the points. Multiplying x2 by 2 makes the basic parabola steeper. What?

x y Calculate points from this table. The basic parabola is shown on the graph, dotted blue Draw a parabola through the points. Multiplying x2 by makes the basic parabola wider. What?

y The x2 means the parabola is upside down. What? x

y The 4 means the parabola is moved How? up by 4 units. x

y The –(….)2 means the parabola is upside down. What? x

y x The 2 means the parabola is moved left by 2 units. How?

y The –(….)2 means the parabola is upside down. What? x

The –1 means the parabola is moved right by 1 unit. How? x

The –2 means the parabola is moved How? down by 2 units. x

x y Calculate points from this table & plot. Draw a parabola through the points. The graph shows the parabola cuts the x-axis at 3 and –1. Continued on next slide.

y The x-intercepts can be obtained from the two factors: At x-intercepts, y = 0. Solve. x Coordinates of the x-intercepts are (3,0) and (1,0).

y Factorise Equate to 0 for x-intercepts Solve. Substitute x = 0 for y-intercept Draw a parabola through the points. The line of symmetry of the parabola is halfway between x = 4 and x = 2. x i.e. x = 1. Substitute x = 1 for y-coordinate of vertex The vertex is at

y Equate to 0 for x-intercepts Solve. Substitute x = 0 for y-intercept Draw a parabola through the points. The line of symmetry of the parabola is halfway between x = 0 and x = 4. x i.e. x = 2. Substitute x = 2 for y-coordinate of vertex The vertex is at

y Equate to 0 for x-intercepts Solve. Note: The position of the vertex means the graph must be upside down. Substitute x = 0 for y-intercept Draw a parabola through the points. The line of symmetry of the parabola is halfway between x = 1 and x = 5. x i.e. x = 3. Substitute x = 3 for y-coordinate of vertex The vertex is at