"Parabolas Intro 2020"

2 -2 4 -4 2 -2 4 -4 6 -6 y = y = 1 y = 3 Equations such as (y = some number) have horizontal lines for graphs. Fill in the missing number for the bottom line. 2 -2 4 -4 2 -2 4 -4 6 -6 Equations such as y = mx + b ( y = a number times x + a number) also have lines for graphs. These lines have a slope of ½ y = ½x-1 y = ½x-3 Click OK 2 -2 4 -4 2 -2 4 -4 6 -6 Quadratic equations (equations with 2 as the highest power) are curved. The curve is called a Parabola. The equation y = x Click OK Linear Equation (Line Graph) ? ◡ Quadratic Equation (Parabola graph) ? 2 -2 4 -4 2 -2 4 -4 6 -6 Equation of the graph y =x ^{2}Axis of symmetry Vertex Other points on the parabola Click OK 2 -2 4 -4 2 -2 4 -4 6 -6 Equation of the graph ? y =x ^{2}Axis of symmetry ? Vertex ? Other points on the parabola ? 2 -2 4 -4 2 -2 4 -4 6 -6 A B D E C Which arrow (A, B, C, D, or E) points at the axis of symmetry? 2 -2 4 -4 2 -2 4 -4 6 -6 Axis of symmetry x = -2 ( , ) What are the (x,y) coordinates of the vertex? The VERTEX (turning point) of the graph is always ON the axis of symmetry. 2 -2 4 -4 2 -2 4 -4 6 -6 Axis of symmetry ? Vertex ? Step 1: Find the Axis of symmetry Step 2: Find vertex on the axis of symmetry ( -2, -1 ) 2 -2 4 -4 2 -2 4 -4 6 -6 Axis of symmetry x = -2 ■ ▲ Vertex Step 3: Plug x values into the equation of the parabola, y = x ^{2 }+ 4x + 3to plot other points on the parabola. ( -2, -1 ) Click OK 2 -2 4 -4 2 -2 4 -4 6 -6 Axis of symmetry x = -2 ▲ ? ■ ? ■ ▲ Vertex Step 4: Reflect (fold) the other points over the axis of symmetry. Drag the reflected points to the correct location ( -2, -1 ) 2 -2 4 -4 2 -2 4 -4 6 -6 Axis of symmetry x = -2 ? ▲ ■ ■ ▲ Vertex (The Axis of symmetry equation is the vertex' x-coordinate) ( -2, -1 ) ? You have plotted 5 points on the parabola Step 2 Step 1 Step 3 Step 4 ◡ ◡ Use the axis of symmetry to find the VERTEX ? Find the AXIS OF SYMMETRY (SUCH AS X = 3) ? Plot 2 other points by plugging new x values in the original equation (such as y = x ^{2} + 8x - 20) ? Reflect the 2 points over the axis of symmetry for a total of 5 points (including the vertex) ? ◡ Graphing Parabolas ◡ ◡ ◡ ◡ ◡ ◡ ◡ ◡ The End ◡ ● ◒ |

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