Investigating Characteristics of Quadratic Functions Part 1 What

Investigating Characteristics of Quadratic Functions Part 1

What have we already seen? We have seen equations in these forms. 1. y = x² 2. y = -3 x² 3. y = -0. 5 x² + 4

Some look like these and are trinomials. y = x² + 2 x + 1 y = -x² - 3 x – 6 These are quadratic equations written in standard form. The standard form of a quadratic equation is y = ax² + bx + c

Look at some characteristics y = x² + 4 x + 3 Y-intercept Vertex

Let’s graph a couple of these and look at the vertex and y-intercept y = x² + 2 x + 1

Another graph… y = x² + 2 x + 6

And Another… y = -3 x² + 6 x - 2

Axis of Symmetry � The axis of symmetry is the vertical line that passes through the vertex. Now go back to the graphs and draw in the axis of symmetry.

How can we find the vertex of a quadratic function without graphing it? From standard form y = ax² + bx + c y = x² + 2 x + 3 1. Find 2. Plug that in for x in the equation to find y. 3. Be sure to write the vertex as an ordered pair (x, y).

Try a few of these… Find the vertex. 1. y = 3 x² + 6 x - 2 2. y = -x² - 4 x = 4

Now let’s look at the y-intercept � What � How is the y-intercept of a parabola? do you find the y-intercept on a graph? would you find the y-intercept of a parabola if you don’t graph it but you have the equation?

More on the y-intercept � How would you find the y-intercept of a parabola if you don’t graph it but you have the equation? �Example: y = x² + 2 x + 3 1. Let x = 0 2. Plug 0 in everywhere there is an x and solve for y. 3. Be sure to write the y-intercept as an ordered pair (x, y).

Try a few of these… Find the y-intercept 1. y = 4 x² - x + 1 2. y = -x² + 4 x + 4