Quadratic Relationships

Standard Form

Learning Goals

-Learn how to use the standard form formula to solve problems

-Find a,b and c in the standard form equation

-Use the Quadratic Formula to find x-intercepts

-Find AOS (Axis of Symmetry) to plot the parabola or find the Max or Min

-Change standard form into vertex form by completing the square

y = ax^2 + bx + c

Summary

  • the value of a gives you the shape and direction of opening
  • the value of c is the y-intercept
  • Solve using the quadratic formula, to get the x-intercepts
  • Complete the square to get vertex form
  • X-intercepts and AOS
  • Plug in AOS to find MAX OR MIN

Completing the Square Example

Equation: x^2-8x+24=0

Move 24 to the other side: x^2-8x=-24

Divide b/2 then square root: (-8/2= 4, 4^2= 16) x^2-8x+16=-24+16

Vertex Form: (x-4)^2=-8

Solving Quadratic Equations using the Quadratic Formula - Example 1
Completing the Square to Solve Quadratic Equations: More Examples - 1
Example 4: Applying the quadratic formula | Quadratic equations | Algebra I | Khan Academy