Quadratic graphs

Write x 2 + 12 x + 50 in the form (x + a) 2 + b where a and b are integers.

A curve has the equation y = (x – 3) 2 – 8

Write down the coordinates of the turning point of the curve.

A roller coaster starts at ground level. The height above ground level, h, in metres, of the roller coaster is given by

where t is the time in seconds after the roller coaster starts.

Sam draws a graph of h against t for 0 t 14

Make two criticisms of Sam’s graph.

Express x² + 8x – 5 in the form (x + a)² – b where a and b are integers.

A curve has the equation y = (x – 7)² + 8

Write down the coordinates of the turning point of the curve.

The nth term of a sequence is n² – 30n + 236

By completing the square, show that all the terms of the sequence have two or more digits.

Here is a sketch of the graph y = – 2 x + 6

Complete the coordinates of C and D.

Here is a sketch of a quadratic graph.

Complete the following statements.

Here is a sketch of the graph y = – 2 x + 6

Complete the coordinates of C and D.

Here is a sketch of a quadratic graph.

Complete the following statements.

Here is a quadratic graph with equation y = f(x)

Write down the roots of the equation f(x) = 0

Write 2 x 2 – 12 x + 7 in the form d (x + e) 2 + f where d, e and f are integers.

Here is the graph of y = 0.5x² – 6x + 12

Use the graph to estimate the solutions of 0.5x² – 6x + 12 = 0

Here is a sketch of the quadratic graph y = f(x) The graph crosses the x-axis at x = a and x = b

Write an expression for the x-coordinate of the turning point.

Express x² – 6x – 15 in the form (x – a)² – b where a and b are integers.

The equation of a curve is y = x² – 18x + 70 By completing the square, work out the coordinates of the turning point. You must show your working.

Here is a sketch of the curve y = x² – 4x – 5

Write down the two roots of x² – 4x – 5 = 0

Work out the coordinates of T, the turning point of the curve.

Here is a sketch of the curve y = x² – 4x – 5

Write down the two roots of x² – 4x – 5 = 0

Work out the coordinates of T, the turning point of the curve.

The equation of a curve is y = x² + 14x + 52 By completing the square, work out the coordinates of the turning point. You must show your working.

Here is the graph of y = x² – 7x + 10 for values of x from 0 to 7

Write down the roots of x 2 – 7 x + 10 = 0

Write down the x-coordinate of the turning point of the curve.

Here is the graph of y = x² – 7x + 10 for values of x from 0 to 7

Write down the roots of x 2 – 7 x + 10 = 0

Write down the x-coordinate of the turning point of the curve.

The equation of a curve is y = (x – 1) 2 – 6 Circle the coordinates of the turning point.

(– 1, – 6) (1, 6) (– 1, 6) (1, – 6)

A curve has the equation y = x² – 6x + 17 The turning point of the curve is at (a, 8)

By completing the square, or otherwise, work out the value of a.

The turning point of the curve y = x 2 + 4 x + b also has y-coordinate 8 Work out the value of b.

The only solution to x² + bx + c = 0 is x = 5 Work out the values of b and c.

The turning point of the graph y = (x + a)² + b has x-coordinate –2 (3, 1) is another point on the graph. Work out the y-coordinate of the turning point.

Circle the point that lies on the curve y = x² – 4x + 1

(–1, 4) (–1, –4) (–1, –2) (–1, 6)

Here is a quadratic graph.

Circle the x-coordinate of the turning point of the graph.

–4 –1 1 3

Here is a sketch of a quadratic curve. The turning point is (3, –2)

Circle the correct statement about the gradient of the curve for x < 3

gradient is positive gradient is negative

gradient is zero gradient could be any value

The equation of a curve is y = (x + 3)² + 5 Circle the coordinates of the turning point. (5, 3) (5, –3) (3, 5) (–3, 5)

Here is the graph of y = f(x) where f(x) is a quadratic function.

Write down all the integer solutions of f(x) 0

Complete the table of values for y = x² x − 2

x	2	1	0	1	2	3
y			2	2		4

Draw the graph of y = x² − x − 2 for values of x from 2 to 3

Write down the x-coordinate of the turning point of the graph.

Here is a sketch of y = f(x) where f(x) is a quadratic function. The graph intersects the x-axis where x = –2.5 and x = 1

Circle the solution of f(x) > 0

x < –2.5 or x > 1 x > –2.5 or x > 1

–2.5 < x < 1 x > –2.5 or x < 1

Here is a sketch of y = x² + bx + c The curve intersects the x-axis at (5, 0) and point P the y-axis at (0, –10)

Work out the x-coordinate of the turning point of the graph.