GCSE Solving Quadratic Equations 5

Question 1

What is the axis of symmetry of the parabola y = 2x² − 8x + 3?

Accepted Answer

x = 2

Answer

Axis of symmetry: x = −b/(2a) = 8/4 = 2.

Question 2

Solve x² − 2x − 8 = 0 using the quadratic formula.

Accepted Answer

x = 4 and x = −2

Answer

x = (2 ± √36) / 2 = (2 ± 6) / 2, giving x = 4 or x = −2.

Question 3

If the roots of a quadratic are x = 5 and x = −3, which equation fits?

Accepted Answer

x² − 2x − 15 = 0

Answer

Sum of roots = 2, product = −15, so the equation is x² − 2x − 15 = 0.

Question 4

Solve (x − 3)² = 25.

Accepted Answer

x = 8 and x = −2

Answer

x − 3 = ±5, so x = 8 or x = −2.

Question 5

Which quadratic equation has roots that are both negative?

Accepted Answer

x² + 5x + 6 = 0

Answer

x² + 5x + 6 = (x + 2)(x + 3) = 0 gives x = −2 and x = −3, both negative.

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