The parabola with equation y = kx² − x + 30 passes through the point (5, 0). What is the value of k?
A) −2
B) 1
C) 3
D) 2
E) −1
IMAT 2026 · Question 59
Q59 - Algebraic equations
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The correct answer is E) −1.
If the parabola passes through (5, 0), then x = 5 and y = 0 must satisfy the equation:
0 = k × 5² − 5 + 30
0 = 25k + 25 → k = −1
Check: y = −x² − x + 30 at x = 5 gives −25 − 5 + 30 = 0 ✓.
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