The quadratic function
Answers are for parents and teachers.
1
Find the vertex and the y-intercept of f(x) = x² + 6x + 4.
x = −6/2 = −3; f(−3) = 9 − 18 + 4 = −5. Vertex (−3, −5); y-intercept 4.
2
Make a table for f(x) = −x² + 2x + 3 with x from −2 to 4. What is the maximum value?
f = −5, 0, 3, 4, 3, 0, −5. Vertex (1, 4); maximum value 4.
3
For which m is f(x) = (m + 2)x² − x + 1 quadratic?
m + 2 ≠ 0, so m ≠ −2.
4
Write f(x) = 2x² − 8x + 3 in vertex form.
x = 8/4 = 2; f(2) = 8 − 16 + 3 = −5. So f(x) = 2(x − 2)² − 5. Check: 2(x² − 4x + 4) − 5 = 2x² − 8x + 3 ✓.
5
A stone thrown from the ground has height h(t) = 30t − 5t² metres. Find its greatest height and the time it lands.
t = 30/10 = 3 s, h(3) = 90 − 45 = 45 m. It lands when 5t(6 − t) = 0, so t = 6 s.