Back to Solve linear-quadratic systems — Problem 1 · Task Set 44

Exercises: Solve Linear-Quadratic Systems

Show all algebraic steps. For each solution (x, y), verify in both original equations.

Grade 10·17 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-c-7

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Recall / Warm-Up

$Three side-by-side diagrams showing a line and parabola with 2 intersections, 1 tangent point, and 0 intersections.$

The diagram below shows three cases for a line intersecting a parabola. How many intersection points does a line and a parabola have in the tangent case?

0 — the line misses the parabola entirely

1 — the line touches the parabola at exactly one point

2 — the line crosses the parabola twice

Infinitely many — the line lies along the parabola