1 / 11

Graphs parabolas by calculating strategic points

Graphs parabolas by calculating strategic points. Strategic points to calculate. Establish orientation of parabola Axis of Symmetry Vertex Roots y- intercept If you do not have 5 points substitute a value for x and calculate the corresponding y. Parabolas. y = ax 2 + bx + c

levi-mcguire
Download Presentation

Graphs parabolas by calculating strategic points

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Graphs parabolas by calculating strategic points

  2. Strategic points to calculate • Establish orientation of parabola • Axis of Symmetry • Vertex • Roots • y- intercept • If you do not have 5 points substitute a value for x and calculate the corresponding y

  3. Parabolas y = ax2 + bx + c When the coefficient of x2 is positive the graph is -shaped. When the coefficient of x2 is negative the graph is -shaped.

  4. Graphs of the form y = ax2 + bx + c

  5. Parabolas …and a turning point called the vertex. Parabolas have a vertical axis of symmetry … The axis of symmetry is a vertical line The equation of a the axis of symmetry is EC The vertex is located on the axis of symmetry – it has a x-coordinate of Find the y-coordinate by plugging in for x

  6. Sketching graphs of quadratic functions The quadratic function y = ax2 + bx + c will cross the y-axis at the point (0, c). Sketch the graph of the function y = x2 – 2x – 3. y = 2x2 – 5x – 3 c = – 3 The parabola crosses the y-axis at the point (0, –3). Axis of symmetry: Vertex

  7. Sketching graphs of quadratic functions When a quadratic function factors we can use its factored form to find where it crosses the x-axis. For example: Sketch the graph of the function y = x2 – 2x – 3. The function crosses the x-axis when y = 0. x2 – 2x – 3 = 0 (x + 1)(x – 3) = 0 x + 1 = 0 or x – 3 = 0 x = –1 x = 3 The function crosses the x-axis at the points (–1, 0) and (3, 0).

  8. Sketching graphs of quadratic functions (3, 0) (–1, 0) y (0, –3) (1, –4) 0 x We can now sketch the graph. • Establish orientation of parabola: open up • Axis of Symmetry x=1 • Vertex (1,-4) • y- intercept y=-3 • Roots x=-1 or x=3

  9. Sketching graphs of quadratic functions In general: When a quadratic function is written in the form y = a(x – p)(x – q), it is called factored form and p and q are the roots of the quadratic function.

  10. Graphs of the form y = a(x – p)(x – q)

  11. You try • Find • Establish orientation of parabola • Axis of Symmetry • Vertex • Roots • y- intercept Then graph the parabola

More Related