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Maths-

General

Easy

Question

The graph of the function f defined by $f left parenthesis x right parenthesis equals 1 fourth left parenthesis x plus 4 right parenthesis squared minus 5$ is shown. The graph passes through the points $left parenthesis negative 10 comma a right parenthesis text and end text left parenthesis a comma b right parenthesis comma$ where a and b are constants. What is the value of b ?

4
9
11
16

The correct answer is: 11

HINT : find a by substituting the point (-10,a) and value of ‘b’ by substituting (a, b) in the given equation.
Step 1: substitute (-10,a) in equation $y equals 1 fourth left parenthesis x plus 4 right parenthesis squared minus 5$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell y equals 1 fourth left parenthesis negative 10 plus 4 right parenthesis squared minus 5 end cell row cell a equals 1 fourth left parenthesis negative 6 right parenthesis squared minus 5 end cell row cell a equals 1 fourth space cross times space 36 minus 5 end cell row cell a equals 9 minus 5 not stretchy rightwards double arrow a equals 4 end cell end table$

Step 2 :substitute (a,b)[i.e (4,b)] in equation $y equals 1 fourth left parenthesis x plus 4 right parenthesis squared minus 5$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell b equals 1 fourth left parenthesis 4 plus 4 right parenthesis squared minus 5 end cell row cell b equals 1 fourth space cross times space 64 minus 5 end cell row cell b equals 16 minus 5 not stretchy rightwards double arrow b equals 11 end cell row cell therefore bold b equals 11 end cell end table$

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