Question

Sktech, on seperate diagrams, the graphs of each of the following, showing the x- and y-intercepts and also state the coordinates of the maximum or minimum points.

1. y = (x - 1)(x + 7)
2. y = (x + 2)(x - 5)
3. y = 3x^2 - 8x

Could someone help me with this? Thx. (:

Answer 1

They are equations of parabolas. The maximum or minimum will be at the vertex. The x and y itercepts will be where the parabola crosses the x and y axis.

Use the foil method to turn the two factors into an equation. So equation 1 will look like this.

\[(x-1)(x+7)=y\]\[x ^{2}+7x-x-7=y\]\[x ^{2}+6x-7=y\]

Use geogebra or a graphing calculator to graph each of the equations.

http://www.geogebra.org/cms/

Answer 2

Since the vertex is the maximum or minimum, use the vertex formula to find the x value of the vertex.

-b/2a

The x intercepts occur when y=0 and the y intercept occurs when x=0.