Quadratic Equations In Vertex Form - Education Ti printable pdf download

Quadratic Equations In Vertex Form - Education Ti

QUADRATIC EQUATIONS IN VERTEX FORM

y = a(x-h)²+k

Any quadratic equation can be expressed in the form

. This is

called the vertex form of a quadratic equation. The graph of a quadratic equation forms a

parabola. The width, direction, and vertex of the parabola can all be found from this

equation.

The value of a

The value of

tells us if the parabola opens upward or downward. If

is positive the

parabola opens upward. If

is negative the parabola opens downward. The value of

also indicates the width of a parabola. When we talk about how wide or narrow a

parabola is, we are comparing the parabola to the parent quadratic function of

y = x²

a=1

, which has a standard width of

. The smaller the absolute value of

, the

wider the parabola will be. Use your calculator to graph the parent function, y = x².

Then, graph the following four quadratic equations on your calculator and compare their

widths to the standard width of the parent graph.

1. y = 2x²

Twice as wide or twice as narrow? _______________________

2. y = 1/3x²

3 times wider or 3 times narrower? _______________________

3. y = -5x²

5 times wider or 5 times narrower? _______________________

4. y = 1/4x²

4 times wider or 4 times narrower? _______________________

Quadratic Equations In Vertex Form - Education Ti