Introduction to Quadratics Mr. Daniels

Quadratic Equations I What is a quadratic equation? A quadratic equation in standard form: This exponent makes the equation quadratic The values a, b and c are constants and have special meaning that we will explain

Properties of Quadratic Equations How does a quadratic equation look? a = 1 b = 6 c = 9 Axis of Symmetry (divides the quadratic in half) Determined by the formula –b/2a x = -3 Parabola (the graph of a quadratic) Vertex (the lowest or highest point of the quadratic) Has an x and y coordinate x coordinate is –b/2a y coordinate is determined by substitution in the quadratic equation Vertex (-3, 0)

Examples 1 & 2

Examples 3 & 4

We Do - Examples 5 & 6

You Do - Examples 7 & 8

You Do - Examples 9 & 10

More Properties of Quadratic Equations What else do we know about quadratics? Vertex is the maximum value or highest point of the quadratic Concave Down Concave Up Vertex is the minimum value or lowest point of the quadratic

Even More Properties of Quadratic Equations What else can learn from quadratics? y-axis y-intercept (same as c) y = 12 a = 1 ; Concave Up Crosses the x-axis twice x = 3 x = 4 x-axis Roots or Solutions (can be 0, 1, or 2 roots)

Quadratic Equations Summary Parabola in standard form: y = ax2 + bx + c Axis of Symmetry divides the quadratic exactly in half Vertex is the lowest or highest point of the quadratic and has an x and a y value (x, y) If quadratic is Concave Up it has a Minimum If quadratic is Concave Down it has a Maximum Roots or Solutions are the values of x where the quadratic crosses the y-axis There can be 0, 1, or 2 roots for a quadratic The y-intercept is y = c

The End