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Quadratics & Parabolas (Foundations)

Core skills for this exam family.

Phase 2 · SAT Math

FoundationsStandardAdvanced

Quadratics & Parabolas: core idea

Vieta for sum/product of roots.

Example problem: hint and answer

Factor x2+7x+12x^2+7x+12.

Hint: Find two numbers with product 12 and sum 7. Answer: (x+3)(x+4).

Practice (9 problems — type your answers)

  • 1. Solve x2=49x^2=49. Give the positive solution.

  • 2. What is the yy-intercept of y=x2−5x+2y=x^2-5x+2?

  • 3. For y=(x−3)2+1y=(x-3)^2+1, what is the vertex?

  • 4. Find the roots of x2−9x=0x^2-9x=0.

  • 5. The parabola y=−2x2+6x−1y=-2x^2+6x-1 opens in which direction?

  • 6. Evaluate f(−2)f(-2) if f(x)=x2+4x−3f(x)=x^2+4x-3.

  • 7. What is the axis of symmetry of y=(x+5)2−8y=(x+5)^2-8?

  • 8. Expand (x+4)(x−4)(x+4)(x-4).

  • 9. A square has area 121121. What is its side length?

Quadratics & Parabolas Practice Problems — Foundations