Algebra I Lesson

The Master Key: The Quadratic Formula and The Discriminant

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8th or 9th GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.HSA.REI.B.4b, CCSS.MATH.CONTENT.HSA.REI.B.4a60 min

Learning Objective

Students will be able to calculate the discriminant $b^{2} - 4 a c$ to determine the number of real solutions of a quadratic equation, apply the Quadratic Formula to solve any quadratic in standard form (including cases requiring rearrangement), and connect discriminant sign to the graph of the corresponding parabola.

Lesson Overview

Students discover how the discriminant $b^{2} - 4 a c$ predicts the number of x-intercepts of a parabola before solving, then master the full Quadratic Formula across increasingly complex quadratics — including irrational roots, rearranging to standard form, and a real-world projectile context.

Materials

Vertical non-permanent surfaces (whiteboards, windows with dry-erase markers, or chart paper)
One dry-erase marker per group
Erasers or paper towels
Random grouping cards or app (e.g., Flippity)
Desmos graphing access (teacher display or student devices)
Four-Quadrant note-taking template (half-sheet, one per student)
Exit slip half-sheets

Scaffolded Task Progression

1Task 1

Low-Floor Launch (Anchored Problem — Verbatim): 'Look at the expression inside the radical:

D = b^{2} - 4 a c

. For the quadratic equation

x^{2} - 6 x + 5 = 0

, identify

a

b

, and

c

. Calculate

D

. Is

D

positive, zero, or negative? How many times will this parabola cross the x-axis?'

2Task 2

Slice 1 — Full Formula Launch: Now plug your values of

a

b

c

, and your calculated

D = 16

into the full Quadratic Formula:

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

Solve for both values of

x

. Check: do your answers match what you would get by factoring

(x - 1) (x - 5) = 0

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