If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Unit 14: Quadratic functions & equations

We've seen linear and exponential functions, and now we're ready for quadratic functions. We'll explore how these functions and the parabolas they produce can be used to solve real-world problems.

## Intro to parabolas

• Parabolas intro (Opens a modal)
• Interpreting a parabola in context (Opens a modal)
• Interpret a quadratic graph (Opens a modal)
• Parabolas intro Get 3 of 4 questions to level up!
• Interpret parabolas in context Get 3 of 4 questions to level up!
• Interpret a quadratic graph Get 3 of 4 questions to level up!

## Solving and graphing with factored form

• Zero product property (Opens a modal)
• Graphing quadratics in factored form (Opens a modal)
• Quadratic word problems (factored form) (Opens a modal)
• Zero product property Get 3 of 4 questions to level up!
• Graph quadratics in factored form Get 3 of 4 questions to level up!
• Quadratic word problems (factored form) Get 3 of 4 questions to level up!

## Solving by taking the square root

• Solving quadratics by taking square roots (Opens a modal)
• Solving quadratics by taking square roots examples (Opens a modal)
• Quadratics by taking square roots: strategy (Opens a modal)
• Solving quadratics by taking square roots: with steps (Opens a modal)
• Solving simple quadratics review (Opens a modal)
• Quadratics by taking square roots (intro) Get 3 of 4 questions to level up!
• Quadratics by taking square roots Get 3 of 4 questions to level up!
• Quadratics by taking square roots: strategy Get 3 of 4 questions to level up!
• Quadratics by taking square roots: with steps Get 3 of 4 questions to level up!

## Vertex form

• Vertex form introduction (Opens a modal)
• Graphing quadratics: vertex form (Opens a modal)
• Quadratic word problems (vertex form) (Opens a modal)
• Graph quadratics in vertex form Get 3 of 4 questions to level up!
• Quadratic word problems (vertex form) Get 3 of 4 questions to level up!

• Solving quadratics by factoring (Opens a modal)
• Solving quadratics by factoring: leading coefficient ≠ 1 (Opens a modal)
• Solving quadratics using structure (Opens a modal)
• Quadratic equations word problem: triangle dimensions (Opens a modal)
• Quadratic equations word problem: box dimensions (Opens a modal)
• Solving quadratics by factoring review (Opens a modal)
• Quadratics by factoring (intro) Get 3 of 4 questions to level up!
• Quadratics by factoring Get 3 of 4 questions to level up!
• Solve equations using structure Get 3 of 4 questions to level up!

• The quadratic formula (Opens a modal)
• Understanding the quadratic formula (Opens a modal)
• Worked example: quadratic formula (example 2) (Opens a modal)
• Worked example: quadratic formula (negative coefficients) (Opens a modal)
• Using the quadratic formula: number of solutions (Opens a modal)
• Quadratic formula review (Opens a modal)
• Discriminant review (Opens a modal)
• Quadratic formula Get 3 of 4 questions to level up!
• Number of solutions of quadratic equations Get 3 of 4 questions to level up!

## Completing the square intro

• Completing the square (Opens a modal)
• Worked example: Completing the square (intro) (Opens a modal)
• Worked example: Rewriting expressions by completing the square (Opens a modal)
• Worked example: Rewriting & solving equations by completing the square (Opens a modal)
• Completing the square (intro) Get 3 of 4 questions to level up!
• Completing the square (intermediate) Get 3 of 4 questions to level up!

## More on completing the square

• Solve by completing the square: Integer solutions (Opens a modal)
• Solve by completing the square: Non-integer solutions (Opens a modal)
• Worked example: completing the square (leading coefficient ≠ 1) (Opens a modal)
• Solving quadratics by completing the square: no solution (Opens a modal)
• Proof of the quadratic formula (Opens a modal)
• Solving quadratics by completing the square (Opens a modal)
• Completing the square review (Opens a modal)
• Quadratic formula proof review (Opens a modal)
• Solve equations by completing the square Get 3 of 4 questions to level up!
• Completing the square Get 3 of 4 questions to level up!

## Strategizing to solve quadratic equations

• Strategy in solving quadratic equations (Opens a modal)
• Strategy in solving quadratics Get 3 of 4 questions to level up!

• Finding the vertex of a parabola in standard form (Opens a modal)
• Graphing quadratics: standard form (Opens a modal)
• Quadratic word problem: ball (Opens a modal)
• Graph quadratics in standard form Get 3 of 4 questions to level up!
• Quadratic word problems (standard form) Get 3 of 4 questions to level up!

## Features & forms of quadratic functions

• Forms & features of quadratic functions (Opens a modal)
• Worked examples: Forms & features of quadratic functions (Opens a modal)
• Vertex & axis of symmetry of a parabola (Opens a modal)
• Finding features of quadratic functions (Opens a modal)
• Interpret quadratic models: Factored form (Opens a modal)
• Interpret quadratic models: Vertex form (Opens a modal)
• Graphing quadratics review (Opens a modal)
• Creativity break: How does creativity play a role in your everyday life? (Opens a modal)
• Features of quadratic functions: strategy Get 3 of 4 questions to level up!
• Features of quadratic functions Get 3 of 4 questions to level up!
• Graph parabolas in all forms Get 3 of 4 questions to level up!
• Interpret quadratic models Get 3 of 4 questions to level up!

• Comparing features of quadratic functions (Opens a modal)
• Comparing maximum points of quadratic functions (Opens a modal)
• Compare quadratic functions Get 3 of 4 questions to level up!