Quadratic Functions

Basics of Quadratic Functions Project

1st quadratic function: x^2 + 2x +1 (min)

Vertex: (-1,0)Axis of Symmetry: x= -1 Solutions: (-1,0)Y-intercept: (0,1)Domain: all real numbersRange: y 0

X Y-2 1-1 00 11 42 9

2nd quadratic function:-2x^2 - 8x + 5

Vertex: (-2,13)Axis of Symmetry: x= -2Solutions: (-4.5,0) and (.5,0)Y-intercept: (0,5)Domain: all real numbers Range: y 13

X Y-2 13-1 110 51 -5 2 -19

Real World Parabola:This is a maximum or upside down U parabola that would have 2 x intercepts and 1 y intercept on a graph.

You can tell if a graph opens up if the x^2 value (a value) in the equation is positive. If the x^2 value in an equation is negative then then the graph opens down.

Finding axis of symmetry: for both problems you use the formula-b/2a. For number one its -(2)/2(1) which simplifies to -1. For number 2 its -(-8)/2(-2) which simplifies to -2.

Finding the Vertex:Using the answer to the axis of symmetry equation you fill in all the x's in the problem. For #1 you would do (-1)^2 + 2(-1) +1 to get a final answer of 0. For #2 you would do -2(-2)^2 - 8(-2) + 5 to get a final answer of 13. You use the final answers from both and have them serve as the y value in the points. So number one would be (-1,0) and number 2 would be (-2,13).

Factoring #1 and #2