Quadratic Functions Solving by Graphing Quadratic Function Standard

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Quadratic Functions Solving by Graphing

Quadratic Functions Solving by Graphing

Quadratic Function Standard Form: f(x) = ax 2 + bx + c

Quadratic Function Standard Form: f(x) = ax 2 + bx + c

Solving Quadratic Equations To solve, we need to find the value of x when

Solving Quadratic Equations To solve, we need to find the value of x when y = 0 or f(x) = 0. Located at: x-intercepts Referred to as: solutions, zeros, or roots.

Quadratic Solutions The number of real solutions is at most two. No Real Solutions

Quadratic Solutions The number of real solutions is at most two. No Real Solutions One Solution Two Solutions

Identifying Solutions 2 Example f(x) = x - 4 Solutions are x = -2

Identifying Solutions 2 Example f(x) = x - 4 Solutions are x = -2 and x = 2.

Quadratic Function 2 (y = ax + bx + c) • Each will have

Quadratic Function 2 (y = ax + bx + c) • Each will have a vertex: either a maximum or minimum point. • Line of symmetry: divides the graph in two halves

Quadratic Functions parabola The graph of a quadratic function is a: y Vertex If

Quadratic Functions parabola The graph of a quadratic function is a: y Vertex If the parabola opens up, the lowest point is called the vertex (minimum). If the parabola opens down, the vertex is the highest point (maximum). Vertex x

Axis of Symmetry Parabolas are symmetric. Axis of symmetry Axisy of Symmetry x The

Axis of Symmetry Parabolas are symmetric. Axis of symmetry Axisy of Symmetry x The Axis of symmetry ALWAYS passes through the vertex.

Parent Function: 2 f(x) = x • a = 1, b = 0, c

Parent Function: 2 f(x) = x • a = 1, b = 0, c = 0 • Minimum point (0, 0) • Axis of symmetry x=0 y=x 2

What happen if we change the value of a and c ? Y=4 x

What happen if we change the value of a and c ? Y=4 x 2 y=4 x 2+3 y=-3 x 2 y=-4 x 2 -2

Conclusion (y = ax 2+bx+c) • When a is positive Concave (opens up) •

Conclusion (y = ax 2+bx+c) • When a is positive Concave (opens up) • When a is negative, Convex (opens down) • When c is positive, Moves Up • When c is negative, Moves Down

y = ax 2 + bx + c y a>0 x a<0

y = ax 2 + bx + c y a>0 x a<0

Finding the Axis of Symmetry When a quadratic function is in standard form y

Finding the Axis of Symmetry When a quadratic function is in standard form y = ax 2 + bx + c, the equation of the Axis of symmetry is

STEP 1: Find the Axis of symmetry y STEP 2: Make a table of

STEP 1: Find the Axis of symmetry y STEP 2: Make a table of 3 points Axis of Symmetry: Vertex: Min or Max? Roots: Y-intercept: x

y Axis of Symmetry: Vertex: Min or Max? Roots: Y-intercept: x

y Axis of Symmetry: Vertex: Min or Max? Roots: Y-intercept: x