10.1 Quadratic GRAPHS!

10.1 – Quadratic Graphs Goals / “I can…” Graph quadratic functions of the form y = ax Graph quadratic functions of the form y = ax + c 2 2

10.1 – Quadratic Graphs Use your graphing calculators to graph the following equations: y = x y = 3x 2 2

10.1 – Quadratic Graphs The shapes that you found are called parabolas. They are one of the most common and powerful graphs in math and science. A parabola has a standard form of y = ax + bx + c. 2

10.1 – Quadratic Graphs y x The graph of a quadratic function is a parabola. Vertex A parabola can open up or down. If the parabola opens up, the lowest point is called the vertex. If the parabola opens down, the vertex is the highest point. Vertex NOTE: if the parabola opened left or right it would not be a function!

10.1 – Quadratic Graphs Standard Form a > 0 y = ax2 + bx + c The standard form of a quadratic function is y = ax2 + bx + c The parabola will open up when the a value is positive. The parabola will open down when the a value is negative.

The line of symmetry ALWAYS passes through the vertex. 10.1 – Quadratic Graphs Line of Symmetry y x Line of Symmetry Parabolas have a symmetric property to them. If we drew a line down the middle of the parabola, we could fold the parabola in half. We call this line the line of symmetry. Or, if we graphed one side of the parabola, we could “fold” (or REFLECT) it over, the line of symmetry to graph the other side. The line of symmetry ALWAYS passes through the vertex.

10.1 – Quadratic Graphs Each parabola has an axis of symmetry and a vertex. Symmetry cuts an object into two equal parts. A vertex can either be a maximum (highest point) or a minimum (lowest point).

10.1 – Quadratic Graphs Example

10.1 – Quadratic Graphs Example

10.1 – Quadratic Graphs How do the widths of a parabola differ? On your calculator graph y = 4x y = ½ x y = x y = -2x Describe the differences? 2 2 2 2

10.1 – Quadratic Graphs What happens if you graph y = x + 3 and y = x – 2 2 2

10.1 – Quadratic Graphs This is called a vertical shift.

10.1 – Quadratic Graphs 2 The equation y = -16t + x is very powerful. It is for the height an object is when it is dropped from a height of x. (-16t is the force of gravity) 2