## Monday, September 9, 2013

### SP#1: Unit E Concept 1 - Graphing a quadratic and identifying all key parts

Problem:
F(x) = 6x² + 13x - 8

This problem is to see if you can identify the x-intercepts, y-intercepts, vertex(max/min), axis of quadratics and how to graph quadratics using the parent function. Already, just by looking at this problem, you already know that the graph opens up because a is positive.

To continue, you must remember how to complete the square, so you can convert it from standard form to the parent function equation, which would then make it easier for you to graph the function. After that, you can easily solve for x-intercepts, y-intercepts, vertex(max/min), and the axis of symmetry. Be careful with the x-intercepts because sometimes you might have imaginary numbers, but you wouldn't plot it on a graph because there is no axis for them.

Work:

Parent function equation:
y = 6(x + 13/12)^2 - 361/24

Vertex: (-13/12, -361/24) min.

Y-intercept: (0, -8)

X-intercept(s):
(½, 0) and (-8/3, 0)
or
(0.5, 0) and (-2,67, 0)

After you finish the work, all you have to do is to plot the points on the graph and exploit symmetry to graph the quadratic (as shone below).