A quadratic polynomial attains its minimum value at and passes through the point .

MATHEMATICS · Multi-part · AoPS · Mathematics · Graphing Quadratics · Graphing Quadratics

Problem

A quadratic polynomial attains its minimum value

3

x = 2

and passes through the point

(0,7)

. (i) Write the polynomial in the form

y = a(x-h)^{2}+k

using the given minimum point. (ii) Determine the value of

a

with the help of the point

(0,7)

and hence express the polynomial in standard form

ax^{2}+bx+c

. (iii) Find the zeros of the polynomial, if any exist. (iv) Draw a complete sketch of the graph, labelling the vertex, the

y

-intercept and the zeros (if any).