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
Quadratic Formula
-Plug in a,b and c to find x-intercepts
-Find AOS using the intercepts
-Solve a word problem
Standard Form to Vertex Form
-Complete the square and graph the parabola
Find A,B and C
-Plug in the values into the quadratic formula to find x-intercepts
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