A Cartesian plane has an $x$x-axis ranging from $0$0 to $18$18 and a $y$y-axis ranging from $-18$−18 to $18$18. The $x$x-axis has major tick marks at $6$6-unit intervals, while the $y$y-axis has no explicitly labeled tick marks. A parabola that opens upward is plotted on the Cartesian plane. The parabola descends from the upper left and intersects the $x$x-axis at point $\left(6,0\right)$(6,0) before reaching the vertex. From the vertex, the parabola ascends toward the upper right and intersects the $x$x-axis at point $\left(12,0\right)$(12,0). The points and their coordinates are not explicitly given nor labeled.

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.

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

Give your answer as an inequality.

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

Give your answer as an inequality.

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

Easy

3 min

The function $f\left(x\right)=5+4x-x^2$f(x)=5+4x−x2 has been graphed.

Use the graph to solve the inequality $5+4x-x^2>0$5+4x−x2>0.

Easy

1 min

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

Easy

2 min

Consider the function $f\left(x\right)=x^2-4x-5$f(x)=x2−4x−5.

Easy

3 min

Outcomes

MA12-1

uses detailed algebraic and graphical techniques to critically construct, model and evaluate arguments in a range of familiar and unfamiliar contexts

1.035 Solving quadratic inequalities graphically

Interactive practice questions

Outcomes

MA12-1

What is Mathspace

About Mathspace