Vertex Form of Quadratics We already know We

Vertex Form of Quadratics

We already know: We are learning today:

Why is knowing vertex form important if we already know standard form? ? If an equation is in vertex form you should be able to state the axis of symmetry & vertex form with no work.

This is a HIGHLY questioned area of the EOC we will take at the end of the year. It will typically appear on the NO CALCULATOR section.

Let’s make connections: Graph: Direction: Down Axis of Symmetry: Vertex: (2, 4) 2

Let’s make connections: Graph: Direction: Down Axis of Symmetry: Vertex: (-5, -3) -5

Let’s make connections: Graph: Direction: Up Axis of Symmetry: Vertex: (-2, -1) -2

Let’s make connections: Based off our answer for the last three questions what does each part of vertex form mean? a: Direction (up or down – positive or negative) Axis of Sym. is OPPOSITE h: of that number k: Vertex is (-h, k)

A FUN way to remember what “h” does is…. The HOP-posite! H is the OPPOSITE of the axis of symmetry.

Name the direction, axis of symmetry and vertex of each equation. WITHOUT A CALCULATOR. Direction: UP Axis of Sym. : Vertex: -1 (-1, 4) Direction: DOWN Axis of Sym. : Vertex: 7 (7, -2)

Name the direction, axis of symmetry and vertex of each equation. WITHOUT A CALCULATOR. Direction: DOWN Axis of Sym. : Vertex: -4 (-4, 1) Direction: UP Axis of Sym. : Vertex: 2 (2, 0)

Name the direction, axis of symmetry and vertex of each equation. WITHOUT A CALCULATOR. Direction: UP Axis of Sym. : Vertex: -8 (-8, -2) Direction: UP Axis of Sym. : Vertex: -4 (-4, -9)

Re-writing equations in Vertex form. Steps 1. Keep the same “a” value. 2. Put equation into calculator and find the vertex. 3. Put vertex into equation. – REMEMBER, use the opposite of the x value.

Given the equation written in standard form, re-write the equation in vertex form. •

Given the equation written in standard form, re-write the equation in vertex form. On your own. Add to HW •

Vertex Form HW

Where does the graph start? Does it go up or down? Which one is wider?

You would shift it DOWN 4 spots and to the RIGHT two spots. The vertex is (2, -4) It is the opposite of what is in the parenthesis and then the constant on the end.

Add a constant shifts the graph UP or DOWN. (0, 2) (0, -4) (0, -150)

Normally + means move right, but here it’s the opposite. (-3, 0) (8, 5) (1, 0) (-1, -4) (3, -10)

Graph is shifted down 4 (which eliminates options 3 and 4. Graph is shifted to the right 3 (think “opposite”) so that means minus.

Up, (2, 7) Up, (-1, -7 ) Down, (-6, 4) Down, (-4, -3) Down, (5, 11)

33. 6 meters Max height = 210 meters Reaches the max height in 6 seconds