004 Sample Final A, Problem 2

From Math Wiki
Revision as of 22:46, 31 May 2015 by MathAdmin (talk | contribs) (Created page with "<span class="exam"> a) Find the vertex, standard graphing form, and ''x''-intercepts for <math>f(x) = \frac{1}{3}x^2 + 2x - 3</math><br> b) Sketch the graph. Provide the ''y''...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

a) Find the vertex, standard graphing form, and x-intercepts for
b) Sketch the graph. Provide the y-intercept.

Foundations
1) What is the standard graphing form of a parabola?
2) What is the vertex of a parabola?
3) What is the -intercept?
Answer:
1) Standard graphing form is .
2) Using the standard graphing form, the vertex is .
3) The -intercept is the point where .


Solution:

Step 1:
First, we put the equation into standard graphing form. Multiplying the equation by 3, we get
.
Step 2:
Completing the square, we get . Dividing by 3 and subtracting 6 on both sides, we have
.
Step 3:
From standard graphing form, we see that the vertex is (-3,-6). Also, to find the intercept, we let . So,
. Solving, we get .
Thus, the two intercepts occur at and .
Step 4:
To find the intercept, we let . So, we get .
Thus, the intercept is (0,-3).
Final Answer:
The vertex is (-3,-6). The equation in standard graphing form is .
The two intercepts are and .
The intercept is (0,-3)

Return to Sample Exam