Modulus graphs of quadratic functions · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Modulus of a quadratic graph — objective 1

Maths4U Original · Short practice

Consider \(y = \left|{\left(x - 19\right)^{2} - 16}\right| + 4\), with \(\displaystyle h=19, d=4, k=4\).

Find the left-hand x-coordinate where \(\displaystyle y=k\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Modulus of a quadratic graph — objective 1

Maths4U Original · Short practice

Consider \(y = \left|{\left(x - 21\right)^{2} - 4}\right| + 1\), with \(\displaystyle h=21, d=2, k=1\).

Find the left-hand x-coordinate where \(\displaystyle y=k\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Modulus of a quadratic graph — objective 2

Maths4U Original · Short practice

Consider \(y = \left|{\left(x - 20\right)^{2} - 25}\right| + 5\), with \(\displaystyle h=20, d=5, k=5\).

Find the right-hand x-coordinate where \(\displaystyle y=k\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Modulus of a quadratic graph — objective 2

Maths4U Original · Short practice

Consider \(y = \left|{\left(x - 21\right)^{2} - 4}\right| + 1\), with \(\displaystyle h=21, d=2, k=1\).

Find the right-hand x-coordinate where \(\displaystyle y=k\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Modulus of a quadratic graph — objective 3

Maths4U Original · Short practice

Consider \(y = \left|{\left(x - 21\right)^{2} - 4}\right| + 1\), with \(\displaystyle h=21, d=2, k=1\).

Find the value of y at \(\displaystyle x=h\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Modulus of a quadratic graph — objective 3

Maths4U Original · Short practice

Consider \(y = \left|{\left(x - 22\right)^{2} - 9}\right| + 2\), with \(\displaystyle h=22, d=3, k=2\).

Find the value of y at \(\displaystyle x=h\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Modulus of a quadratic graph — objective 4

Maths4U Original · Short practice

Consider \(y = \left|{\left(x - 22\right)^{2} - 9}\right| + 2\), with \(\displaystyle h=22, d=3, k=2\).

Find y at \(\displaystyle x=h+d+1\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Modulus of a quadratic graph — objective 4

Maths4U Original · Short practice

Consider \(y = \left|{\left(x - 23\right)^{2} - 16}\right| + 3\), with \(\displaystyle h=23, d=4, k=3\).

Find y at \(\displaystyle x=h+d+1\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →