Advanced Math covers quadratics, exponents, polynomials, and functions — the nonlinear content. This is where 1500+ scores are decided, because the hardest module-2 questions cluster here.
Factored form tells you the zeros. If y = a(x − r₁)(x − r₂), the graph crosses the x-axis at r₁ and r₂. Reading zeros straight from factors saves huge time.
Must-know facts
- Function notation: f(3) means substitute 3 for every x. Don't overthink it.
- Exponent rules: xᵃ · xᵇ = xᵃ⁺ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁰ = 1.
- Vertex of a parabola y = ax² + bx + c is at x = −b/(2a); plug back in for the y-value (the min if a > 0, max if a < 0).
- Sum of the zeros of a quadratic = −b/a; product = c/a. Handy shortcuts.
Desmos tip: A calculator is allowed on the entire Math section — there is no no-calculator portion. You can graph any equation and read zeros, intersections, and vertices directly. Use it to check — but know the algebra for the no-calculator instincts it builds.
Worked examples
Find the zeros of y = x² − 5x + 6.
- Factor: we need two numbers that multiply to 6 and add to −5. Those are −2 and −3.
- So y = (x − 2)(x − 3).
- Set each factor to zero: x − 2 = 0 → x = 2; x − 3 = 0 → x = 3.
- The zeros are x = 2 and x = 3 (the points where the graph crosses the x-axis).
Find the minimum value of y = x² − 6x + 5.
- The graph is a parabola opening upward (a = 1 > 0), so it has a minimum at its vertex.
- Vertex x-coordinate: x = −b / (2a) = −(−6) / (2 × 1) = 3.
- Substitute back: y = 3² − 6(3) + 5 = 9 − 18 + 5 = −4.
- The minimum value is −4, at the point (3, −4).
If f(x) = 2x² − 3x + 1, find f(−2).
- Replace every x with −2: f(−2) = 2(−2)² − 3(−2) + 1.
- Handle the exponent first: (−2)² = 4, so 2(4) = 8.
- Then −3(−2) = +6 (negative times negative is positive).
- Add it up: 8 + 6 + 1 = 15.
Common mistakes to avoid
- Sign errors when substituting a negative number. Remember (−2)² = 4, but −2² = −4.
- Using x = −b/(2a) and stopping there. That gives the x-coordinate; you still have to plug it back in to get the minimum or maximum VALUE.
- Forgetting that the zeros of a(x − r₁)(x − r₂) are r₁ and r₂ — with the opposite sign of what's inside the parentheses.
- Adding exponents when you should multiply: (x³)² = x⁶, but x³ · x² = x⁵.