Quadratic equations and functions

Practice 5 items →

Three tools (factoring, square roots, the formula) and one discriminant. Students solve quadratics, read the number of real roots from D, find vertex, axis, and intercepts, sketch the parabola, and model projectile and area stories.

Specification · for a parent or teacher

Part no.: quadratics-parabolas
Course: High School Math 1 · Unit 9
Realm: Change
Difficulty: 4 of 4 — Grade 7 / Math 1 core. Structure, models, proofs on the grid.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

solve by factoring, square roots, and the formula; read the number of real roots from $D$ ; find vertex, axis, intercepts; sketch from those; model projectile and area stories.

Ready when

$2x^2-3x-2=0$ solved by factoring and formula, and they sketch $y=x^2-4x+3$ from intercepts and vertex.

Formulas

Quadratic formula

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Discriminant

D = b^2 - 4ac

Vertex

x = -\frac{b}{2a}

Watch for

forgetting $\pm$ ; $D$ as “the answer”; vertex formula with $a$ dropped.

Lab

Parabola sliders →Vertex form vs standard; what D < 0 looks like.

Before · requires

Factoring polynomialsfactoring-polynomials · Math 1
Relations and functionsfunction-foundations · Math 1

After · used by

Graphing functionsfunction-features · Math 1

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