Dorchester 2 05-20-2025 Quadratic Review

By Antoinette Norris Woodson

Open Ended

Determine the wordplexers. Write the number then the phrase.

​Quadratic Equations Review
for Algebra II

Why Do We Learn Quadratics?

Purpose • Real-World Application • Careers

Match

Match each quadratic function term to its correct definition.

• Vertex

• Axis of Symmetry

• . Maximum/Minimum

• The x-value(s) where the graph crosses the x-axis; also called roots

• The set of all possible input values (x-values)

The point (x, y) where the axis of symme

vertical line that divides the parabola

The highest or lowest point on the graph

zeroes

Domain

• The point (x, y) where the axis of symme

• vertical line that divides the parabola

• The highest or lowest point on the graph

• zeroes

• Domain

Labeling

Label the graph. Match the correct term or phrase to what it represents.

(below the graph)

Drag labels to their correct position on the image

Maximum

Vertex (5, 2)

Axis of Symmetry: x = 5

Minimum

One zero value

No zero values

Axis of Symmetry: x = 2

Vertex (2, 5)

Labeling

Label the graph. Match the zero smaller and larger values by placing the box on the graph next to what it represents.

Drag labels to their correct position on the image

Vertex (-2, 4)

Minimum

Maximum

Axis of Symmetry: x = -2

Zero smaller value

Zero larger value

Vertex (-4, 2)

Axis of Symmetry: x = -4

Axis of Symmetry: x = 0

Hotspot

Mark the solutions to the quadratic function.

Choose all answers that apply.

Match

Match the following quadratic functions forms to what they most quickly reveal.

• $$f\left(x\right)=2x^2-3x+5$$

• $$f\left(x\right)=2\left(x-4\right)\left(x+3\right)$$

• $$f\left(x\right)=2\left(x-5\right)^2+3$$

y-intercept (0,5)

x-intercepts at x=-3 and x=4

vertex

(5, 3)

• y-intercept (0,5)

• x-intercepts at x=-3 and x=4

• vertex

  (5, 3)

Draw

Complete questions 1 through 5.

The direction of a quadratic describes how it opens: up or down ​

​

"Touches the x-axis"​

• The x-intercept of a parabola is the point where the parabola intersects the x-axis

• A parabola can have one, two or zero x-intercepts

​Notice the y value of the x-intercept is always 0.

Solutions, Zeros, and Roots

• Once we have the x-intercept, we can identify the solutions of the quadratics. They are just the x-value of the x-intercept(s).

• Solutions, zeroes, and roots all mean the same thing!

"Touches the y-axis"​

• The y-intercept of a parabola is the point where the parabola intersects the y-axis

• A parabola will always have one y-intercept.

​Notice how the x value of the y-intercept is always 0.

The "turning point"​

• The vertex of ​a quadratic is the point where the quadratic changes direction

"Cuts the parabola in half"​

• The axis of symmetry is a vertical line that cuts the parabola in half

• The axis of symmetry is always in the form (x = a number)

• The number is the x-value of the vertex

​Domain of a Function

​All possible values that x can be in the graph.

​

​The graph shown keeps going to the left and down... and to the right and down.

​

​This means that eventually ALL x-values will eventually get used in this graph if we keep going. This is why the domain is always "All Real Numbers."

​Range of a Function

​All possible values that y can be in the graph.

​

​The graph shown keeps going to the left and down...

​... and to the right and down.

​

​There are NO points on the graph above y = 4. Therefore the range of this graph is 

Minimum or Maximum​

• The vertex can also be thought as the highest or lowest number.

• The minimum or maximum of a parabola is a number. Specifically, It is the y value of the vertex.

​Each form tells you something different — knowing which one to use depends on what the question is asking!

​ x=-3 and x = 1

​Each form tells you something different — knowing which one to use depends on what the question is asking!

Which Form Is Best for Graphing?

​✅ Vertex Form: y = a(x – h)² + k

​What each part means:

• a → Controls the stretch or compression and whether the parabola opens up or down

• h → Shifts left/right (opposite of sign)

• k → Shifts up/down

• Key Ideas:

  • If a > 1 → graph is narrower (stretched)

  • If 0 < a < 1 → graph is wider (compressed)

  • If a is negative → parabola opens down

Desmos Activity
🧠 Your Mission:
Adjust the quadratic equation to guide the marble through all the stars!

​https://student.desmos.com/activitybuilder/student-greeting/682cbf879973259fb12acccd

• ​Open the activity:

• Click “Start Activity” and follow each level

• Type your equation, then press play

• If the marble misses → revise & retry!