Solve and Graph Quadratic Equation Algebra II

What Shape is the Golden Gate Bridge?

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.

What is a quadratic function?

What is a Parabola?

How to know if it’s a function?

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

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)

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)

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

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