1. Algebra 1 EOC Summer School Lesson 12: Draw Conclusions from Quadratic Graphs

2. Introduction to Quadratic Graphs Quadratic Graphs create a shape called a parabola Every parabola has: – A Vertex – A Maximum or Minimum – An Axis of Symmetry You also might need to find: – X-intercepts – Y-intercept

3. The Vertex The vertex is the lowest or highest point on a parabola. A parabola either opens up or down. If a parabola opens up, it’s vertex is a _____________. If a parabola opens down, it’s vertex is a ____________. minimum maximum

4. Finding the Vertex The vertex is represented by a point on the graph. What is the vertex of this parabola? (-4, -2) Is this vertex a maximum or minimum? minimum

5. Finding the Axis of Symmetry The axis of symmetry is the invisible line that divides the parabola into 2 equal parts. What is the axis of symmetry of this parabola? x = -4

6. x- and y-intercepts The x-intercepts of a parabola are the points where it crosses the x-axis. The y-intercept is the point where the parabola crosses the y-axis. (-3, 0)(1, 0) (0, 4)

7. Parabolas in the Real World Parabolas can be used to model real world problems such as: – The height of a football while being thrown – The height of an object dropped from a high place – The height of a rocket after it is launched

8. Real World Example: The graph shows the height of an object after it is launched. Pay attention to: – The vertex – The y-intercept – The x-intercept Launched from a height of 100 ft. Lands on the ground after 14 seconds Maximum height of 400 ft after 6 seconds

9. A few things about quadratic equations Most quadratic equations are in the form y = ax 2 + c a controls the width of the parabola and whether it opens up or down c controls the y- intercept

10. Talking about a and c If a parabola opened down, the value of a would be __________ If a parabola opened up, the value of a would be __________ If a parabola crossed the y-axis above the origin, the value of c would be ___________. If a parabola crossed the y-axis at the origin, the value of c would be ____________. negative positive More than 0 Equal to 0