Dorchester 2 05-20-2025 Quadratic Review

Why Do We Learn Quadratics?

Purpose • Real-World Application • Careers

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

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"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

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

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

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​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."

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

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

​... and to the right and down.

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​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.

​ x=-3 and x = 1

​✅ Vertex Form: y = a(x – h)² + k

• 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

​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!