1. Solve and Graph Quadratic
Equation
Algebra II

2. What Shape is the Golden Gate Bridge?

3. •What is a quadratic function?
Y = AX^2 + BX + C
•What is a
Parabola?
•How to know if it’s a function?
Use vertical line test.

4. How to find X-intercepts?
X-intercepts: also known as roots, are
the locations where the graph
intersects with the X-axis.
Example: Y = 2X^2 – 8X + 6
Let Y = 0, solve for X:
2X^2 – 8X + 6 = 0
X^2 – 4X + 3 = 0 (simplify)
(X-1)(X-3) = 0 (factor it)
X=1, or X=3

5. How to find Y-intercepts?
Y-intercept: the location where the
graph intersects with the Y-axis.
Example: Y = 2X^2 – 8X + 6
Let 0 = 0, solve for Y:
Y = 2(0)^2 – 8(0) + 6
Y = 0 – 0 + 6 (simplify)
Y=6 (simplify)

6. How to find vertex?
Vertex: the lowest or highest point of the graph.
Example: Y = 2X^2 – 8X + 6, (a=2, b=-8, c=6)
Formula for vertex X= -b/(2a)
X = -(-8)/(2*2)
X = 8/4 = 2 (simplify)
When X=2, Y=2(2)^2-8(2)+6 =8-16+6 =-2
So vertex is (2, -2)

7. How to determine the direction of a
parabola’s opening?
When a>0, parabola opens up
When a<0, parabola opens down
Example: Y = 2X^2 – 8X + 6, (a=2)
Because 2>0, the parabola opens up

8. Graph the Equation:
Domain (x-range): X are all real numbers
Range (Y-range): Y are >= -2