Functions
A quadratic function f(x) = ax² + bx + c draws a parabola. Tasks ask for values, the vertex or the zeros, and they connect directly to quadratic equations.
Generated by the same engine as the Kollego course and solvable without a calculator. Pick an answer in your head, then open the solution.
1. f(x) = 2x² + 2x − 2. Evaluate f(3).
Answer: 22
Substitute and follow order of operations: power first, then products, then sums.
2·3² + 2·3 − 2 = 18 + 6 − 2 = 22.
2. f(x) = x² + 2x − 3. What is the x-coordinate of the vertex?
Answer: -1
For x² + bx + c the vertex is at x = −b / 2.
x = −(2) / 2 = -1.
3. f(x) = 2x² + 3x − 2. Evaluate f(4).
Answer: 42
Substitute and follow order of operations: power first, then products, then sums.
2·4² + 3·4 − 2 = 32 + 12 − 2 = 42.
4. A parabola has zeros at x = -4 and x = 2 and crosses the y-axis at (0 | -8). What is the y-coordinate of its vertex?
Answer: -9
Zero form f(x) = a(x − x₁)(x − x₂); the point on the y-axis gives a; the vertex lies halfway between the zeros.
f(0) = a·(-8) = -8 ⇒ a = 1. Vertex at x = -1: f(-1) = -9.
5. f(x) = x² + 4x + 5. What is the x-coordinate of the vertex?
Answer: -2
For x² + bx + c the vertex is at x = −b / 2.
x = −(4) / 2 = -2.
6. f(x) = 2x² + 3x + 3. Evaluate f(3).
Answer: 30
Substitute and follow order of operations: power first, then products, then sums.
2·3² + 3·3 + 3 = 18 + 9 + 3 = 30.
All maths topics · T-Kurs · M-Kurs · W-Kurs
One diagnostic, a projected score, and your first unit. No card, no time limit on the free tier.
Start free, no card needed