Quadratic Equations

Hong Kong

Stage 4 - Stage 5

Consider the graph of $y=f\left(x\right)$`y`=`f`(`x`).

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a

Find the values of $x$`x` for which $f\left(x\right)=0$`f`(`x`)=0. Write both solutions on the same line separated by a comma.

b

For what values of $x$`x` is $f\left(x\right)<0$`f`(`x`)<0?

Give your answer as an inequality.

c

For what values of $x$`x` is $f\left(x\right)>0$`f`(`x`)>0?

Give your answer as an inequality.

d

What is the $x$`x`-coordinate of the vertex of $f\left(x\right)$`f`(`x`)?

Easy

Approx 4 minutes

Consider the graph of $y=f\left(x\right)$`y`=`f`(`x`).

The function $f\left(x\right)=5+4x-x^2$`f`(`x`)=5+4`x`−`x`2 has been graphed.

Use the graph to solve the inequality $5+4x-x^2>0$5+4`x`−`x`2>0.

Consider the function $f\left(x\right)=x^2-4x-5$`f`(`x`)=`x`2−4`x`−5.

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