Quadratic extrema and roots · 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

Quadratics, roots and extrema — objective 1

Maths4U Original · Short practice

\(f{\left(x \right)} = 3 x^{2} - 108 x + 945\).

Find the x-coordinate of the minimum.

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

Fresh review variant

Quadratics, roots and extrema — objective 1

Maths4U Original · Short practice

\(f{\left(x \right)} = x^{2} - 38 x + 345\).

Find the x-coordinate of the minimum.

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

Method

Quadratics, roots and extrema — objective 2

Maths4U Original · Short practice

\(f{\left(x \right)} = x^{2} - 38 x + 345\).

Find the minimum value.

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

Fresh review variant

Quadratics, roots and extrema — objective 2

Maths4U Original · Short practice

\(f{\left(x \right)} = 2 x^{2} - 80 x + 750\).

Find the minimum value.

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

Apply

Quadratics, roots and extrema — objective 3

Maths4U Original · Short practice

\(f{\left(x \right)} = 2 x^{2} - 80 x + 750\).

Find the larger root.

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

Fresh review variant

Quadratics, roots and extrema — objective 3

Maths4U Original · Short practice

\(f{\left(x \right)} = 3 x^{2} - 126 x + 1311\).

Find the larger root.

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

Check understanding

Quadratics, roots and extrema — objective 4

Maths4U Original · Short practice

\(f{\left(x \right)} = 3 x^{2} - 126 x + 1311\).

Find the discriminant.

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

Fresh review variant

Quadratics, roots and extrema — objective 4

Maths4U Original · Short practice

\(f{\left(x \right)} = x^{2} - 44 x + 475\).

Find the discriminant.

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

Try written exam-style problems →