E XAMPLE 1 Graph = 2 2 + 1 The vertex is (2, 1). Since the x- - - PowerPoint PPT Presentation

DAY 127 – GRAPHING QUADRATICS

GRAPHING PARABOLAS IN VERTEX FORM

Remember, when we’re graphing a parabola, we want to find the vertex first, and then find two

• ther points on either side of the vertex to the

graph so that we get the curved shape we’re all familiar with. When a quadratic equation is in vertex form, the vertex is much easier to find than if the quadratic equation is in standard form.

EXAMPLE 1

Graph 𝑔 𝑦 = 𝑦 − 2 2 + 1

The vertex is (2, 1). Since the x- values for the vertex is “2”. Then for the other x-values, we’ll pick 3 and 4 on the left and 0 and 1 on the right. (The two nearest, nice x-vales to x = 2).

Then, plug in 0, 1, 3, 4 for “x” and see what we get for f(x).

x f(x) 5 1 2 2 1 3 2 4 5

Vertex!

GRAPHING QUADRATIC EQUATION IN INTERCEPT FORM

 Another way to graph quadratics.  Intercept form of a quadratic is its factored form  Example: Intercept form of 𝑔 𝑦 = 𝑦2 − 10𝑦 + 21 is

𝑔 𝑦 = (𝑦 − 7)(𝑦 − 3)

GENERAL RULES FOR GRAPHING QUADRATICS

OF THE FORM 𝑔 𝑦 = 𝑏(𝑦 − 𝑞)(𝑦 − 𝑟) 1) Identify the x-intercept and plot them

• x-intercepts for 𝑔 𝑦 = 𝑏 𝑦 − 𝑞

𝑦 − 𝑟 are (𝑞, 0) and 𝑟, 0 2) Find the vertex and axis of symmetry

• the x-coordinate of the vertex is 𝑦 =

𝑞+𝑟 2

(think about it – it’s located halfway between the zeros)

• plug in the x-coordinate of the vertex to find its y-

coordinate; plot point

• Axis of symmetry is 𝑦 =

𝑞+𝑟 2

GENERAL RULES FOR GRAPHING QUADRATICS

OF THE FORM 𝑔 𝑦 = 𝑏(𝑦 − 𝑞)(𝑦 − 𝑟) 3) Find the y-intercept; reflect over axis of symmetry

• calculate 𝑔(0) to find the y-intercept

4) Find one or two other points if needed, reflecting over axis of symmetry 5) Sketch curve

GENERAL RULES FOR GRAPHING QUADRATICS

OF THE FORM 𝑔 𝑦 = 𝑏(𝑦 − 𝑞)(𝑦 − 𝑟) Example: Graph 𝒈 𝒚 = 𝒚 − 𝟖 𝒚 − 𝟒 1) Identify the x-intercepts and plot them

• x-intercepts are (7, 0) and (3, 0)

2) Find the vertex and axis of symmetry

• 𝑦 =

𝑞+𝑟 2 = 5; 𝑔 5 = −4

• Axis of symmetry is 𝑦 = 5

3) Find the y-intercept; reflect over axis of symmetry

• y-int = 𝑔 0 = 21

GENERAL RULES FOR GRAPHING QUADRATICS

OF THE FORM 𝑔 𝑦 = 𝑏(𝑦 − 𝑞)(𝑦 − 𝑟) 4) Find one or two other points if needed, reflecting over axis of symmetry 5) Sketch curve