Consider the quadratic function

MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

y = 5x^2 + bx + 9

, where

b

is a real constant. (i) Write down the expression for its discriminant in terms of

b

. (ii) Determine the value of

b

for which the graph touches the

x

-axis. (iii) Explain, without further calculation, whether the graph lies entirely above or entirely below the

x

-axis when

b=0