Question

A curve has the equation y = x² + ax + b, where a and b are numbers.

The turning point of the curve is (4, 5).
Work out the values of a and b.

Answer 1

Explanation:

there must be something else missing in the question.

there are many curve like this have same turning point.

Answer 2

• a = -8
• b = 21

Explanation:

You want the standard form monic quadratic equation with turning point (4, 5).

Vertex form

The vertex is (h, k) = (4, 5), and the vertex form equation is ...

y = (x -h)² +k

y = (x -4)² +5

Standard form

y = (x² -8x +16) +5 . . . . expand the square

y = x² -8x +21 . . . . . . . collect terms

The values of 'a' and 'b' are -8 and +21, respectively.