Find f(1) if f(x) = 1x² + 6x + 4.
Answer and explanation
11
1 × (1)² + 6 × (1) + 4 = 11
Subjects
Quadratic equations
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Sample exercises
Find the discriminant of 8x² + 2x + 12 = 0.
Answer and explanation
-380
2² − 4 × 8 × 12 = -380
Find the smaller root of (x − 23)(x − 24) = 0.
Answer and explanation
23
x = 23 or x = 24; 23 < 24
Study notes
Evaluate a quadratic
Square the input before multiplying by its coefficient.
Grades 9–11The discriminant
For real coefficients with a ≠ 0: positive Δ gives two real roots; zero gives one repeated root; negative gives no real roots.
Grades 10–12Roots from factors
Set each factor equal to zero and check the original equation.
Grades 9–11Axis of symmetry
The vertex lies on this vertical axis for y = ax² + bx + c.
Grades 10–12Expand a binomial square
The middle term is twice the product, not zero.
Grades 8–11Complete the square
Halve the coefficient of x, then square it.
Grades 9–12Quadratic equations · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 8–8Quadratic equations · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 9–10Quadratic equations · Formula sheet
Rules, conditions and small examples in one printable reference.
Grades 11–12Quadratics: solving and graphing
A focused reference to use alongside your practice.
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