Do Now: Solve the equation in the complex number system.

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Presentation transcript:

Do Now: Solve the equation in the complex number system.

Academy Algebra II/Trig 4.3: Quadratic Functions & Their Properties HW tonight: p (60-62, 81, 86) HW tomorrow: p (40, 43, 48, 54-55, 87 )

Graphing a quadratic in standard form. Standard form: Shape: parabola Opens up: a is positive Opens down: a is negative Has a vertical line of symmetry through the vertex.

Graphing a quadratic in standard form. Standard form: Find the vertex: (x, y) X-coordinate = Determine the axis of symmetry: Find the y- and x-intercepts. Plot points and sketch parabola. (Optional: choose additional x values and find more coordinates.)

Determine, without graphing, whether the given quadratic has a minimum or maximum value and then find the value.

Graph using its vertex, axis of symmetry, and intercepts. Determine the domain and range and determine where the function is increasing and decreasing.

Graphing a quadratic in vertex. Vertex form: Find the vertex: (h, k) Determine the axis of symmetry: Find the y- and x-intercepts. Plot points and sketch parabola.

Graph using vertex form. Determine the domain and range and determine where the function is increasing and decreasing.

Extension: Determine the quadratic function with vertex (-1, -2) and y-intercept (0, -1).

Extension: Determine the quadratic function with vertex (1, -3) and passes through (3, 5).

Graphing a quadratic in intercept form. (not in your book  ) Intercept form: In this form the quadratic is already factored, so you can replace f(x) with zero and solve the equation to find the x-intercepts. X-coordinate of vertex = average x- intercepts.