Updated Test 1 coverage

Test 1 is Friday, September 25 in class and covers material through Section 2.5. All Section 3.1 topics are excluded, including vertex form, finding vertices, quadratic-function applications, and quadratic regression.

Quiz 4 is a take-home test review assigned Monday, September 21, due September 23 at 3:15 PM. It focuses on Sections 2.4 and 2.5 and includes earlier topics.

This older deck includes supplemental Section 3.1 material. Skip those items for Test 1 and use the updated review page for aligned practice.

Open updated Test 1 review

MATH 130 · Sections 2.5 and 3.1 learning window

Quadratic Equations and Applications

Solve quadratics, interpret vertices, and connect solutions to context

50–55 minutes · Offline capable · Quiz 4 take-home review · Due Sep 23 at 3:15 PM

Learning roadmap and pacing

  1. 1

    write a quadratic in standard form

  2. 2

    choose factoring or the quadratic formula

  3. 3

    find and interpret a quadratic vertex

  4. 4

    reject algebraic answers that do not fit a context

Canvas pacing anchor

Quiz 4 take-home review · Due Sep 23 at 3:15 PM

Sections 2.5 and 3.1 are due Sep 23 at 2:10 PM. Test 1 is Friday, Sep 25 in class

Coverage note

This deck is the sequential study path. Official quiz and test coverage can be adjusted in Canvas or in class.

Activate · 2 minUnit 1 sequence

Entrance retrieval

4 minutes · no notes
  1. Factor $x^2-7x+12$.
  2. Solve $x^2-7x+12=0$.
  3. Does $f(x)=-2x^2+8x+1$ have a maximum or minimum?

Activate · 4 minUnit 1 sequence

Standard form makes the method visible

$ax^2+bx+c=0$, with $a\ne0$

1

Move every term to one side.

2

Combine like terms and identify $a,b,c$.

3

Factor if structure is friendly; otherwise use the quadratic formula.

Explain · 5 minUnit 1 sequence

Model: solve by factoring

Solve $5x^2=-3x+2$.

  1. $5x^2+3x-2=0$.
  2. $(5x-2)(x+1)=0$.
  3. $x=2/5$ or $x=-1$.

Model · 5 minUnit 1 sequence

Quadratic formula: signs need parentheses

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

Write $a$, $b$, and $c$ before substituting, including their signs.

The discriminant $b^2-4ac$ predicts two real, one repeated, or no real solutions.

Explain · 5 minUnit 1 sequence

The vertex answers an optimization question

$h(t)=80t-16t^2$. Find the maximum height.

  1. $a=-16$, $b=80$, so $t=-b/(2a)=2.5$.
  2. $h(2.5)=100$.
  3. Interpret: maximum height is $100$ feet at $2.5$ seconds.

Model · 6 minUnit 1 sequence

Applications require an interpretation check

1

Define the variable and its units.

2

Build or identify the quadratic model.

3

Solve for roots or vertex as requested.

4

Reject times, lengths, or counts that violate the context.

Explain · 4 minUnit 1 sequence

You try: solve and interpret

Work first · then reveal

  1. Solve $2x^2-5x-3=0$.
  2. Find the vertex of $f(x)=2x^2-12x+7$ and state max/min.
  3. A height model has roots $-1$ and $6$. Which time is physically meaningful?

Practice · 5 minUnit 1 sequence

Quiz 4 checkpoint: readiness check

Quiz 4 checkpoint
Closed notes · show complete work
  1. Solve $3x^2+x-2=0$ by factoring.
  2. Use the quadratic formula on $x^2+4x-1=0$.
  3. Find the maximum of $g(t)=-5t^2+30t+4$.
  4. Explain the difference between the vertex time and vertex value.

Assess · 8 minUnit 1 sequence

Exit ticket and next step

Before you leave
  1. Name one skill you can now complete without notes.
  2. Name one error pattern to watch.
  3. Schedule the next short practice before the checkpoint.
Next step

Next: Unit 1E — spaced Test 1 review across all four checkpoints

Synthesize · 3 minUnit 1 sequence