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Maths-

SAT

Easy

Question

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

4
9
11
16

The correct answer is: 11

$f left parenthesis x right parenthesis space equals space 1 fourth open parentheses x plus 4 close parentheses squared minus 5$
(- 10, a) & (a, b) passes through f (x)
$a equals 1 fourth open parentheses negative 10 plus 4 close parentheses squared minus 5 minus 1 fourth open parentheses negative 6 close parentheses squared minus space 5 equals space 1 fourth left parenthesis 36 right parenthesis space minus space 5 equals 9 minus 5 equals 4$
a = 4
(4,b) passes through f (x)
$b equals 1 fourth open parentheses 4 plus 4 close parentheses squared minus space 5$
$equals space 1 fourth 64 minus 5 equals 16 minus 5 equals 11$

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