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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

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strategic points to calculate
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
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.

parabolas1
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

sketching graphs of quadratic functions
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

sketching graphs of quadratic functions1
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).

sketching graphs of quadratic functions2
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
sketching graphs of quadratic functions3
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.

you try
You try
  • Find
  • Establish orientation of parabola
  • Axis of Symmetry
  • Vertex
  • Roots
  • y- intercept

Then graph the parabola