MS 100 College Algebra test six • Name:

Students will be able to... What does it mean to know something? If I ask a class, "Can Layoleen juggle?" how would the class know whether this is true? I could ask a friend of Layoleen. The friend might know, might not. The friend would be a witness, but would that constitute proof? The friend might be biased. Ultimately we would want Layoleen to show us that she knows by taking three objects and keeping them aloft. Maybe Layoleen can only "flash" three - would that count? How well should she juggle to prove that she can do it? Thus the "No she cannot juggle" might be black-and-white true-or-false, but the "Yes she can might have gradations of skill level. So it is in this class. Inability to perform a math skill is fairly clear cut. In the world of academia, this is the meaning to an "F". In this class, an "F" is less than 60% of the points, where points map primarily to tests. Can you algebra? Really?

Ball arc on board, student puts up x and y axis.

1. Find a, b, and c in the y = ax² + bx + c form of the equation for the graph above. The coordinates for both x-intercepts and the vertex are depicted on the graph.

(%i2) solve((0+6)=a*(-14+3)^2,a);
                                         6
(%o2)                              [a = ---]
                                        121
(%i4) expand((6/121)*(x+3)^2-6);
                                  2
                               6 x    36 x   672
(%o4)                          ---- + ---- - ---
                               121    121    121

The quadratic regression is
y = a x^2 + b x +c where:
a = 0.049586776859504134
b = 0.2975206611570248
c = -5.553719008264463
The error is: 8.881784197001252E-16
The correlation coefficient is: 1.0
Source

a = 0.04959
b = 0.2975
c = -5.5537

2. y = -5.5537 Find the y-intercept for the parabola in question number one.

3. p = 5.041667 or 121/24 Find the focus distance p for the parabola in question number one.

4. Write out the standard form for the parabola in question one.
$(y-(-6\left)\right)={\frac{6}{121}(x-(-3\left)\right)}^2$

5. p = 10 Given that $a=\frac{1}{4p}$, determine the focal distance p for y = 0.025x² + 8.2x + 16.4

6. Use a Qalculate! to help you sketch a graph of the following function Sketch the graph on your paper.
$\text{f(x)}=\frac{7x^2-28}{\sqrt{(49-x^2)}}$

7. −4 Determine the y-intercept for the rational function in question six.

8. ±2 Determine the x-intercept(s) for the rational function in question six.

9. ±7 Determine the vertical asymptotes for the rational function in question six.

10. −7 < x < 7 Write out the domain for the rational function in question six.

11. Find the standard form equation for the parabola formed by the shown focus and directrix:

$(y-14)={(x-6)}^2$

reset
set border
set xtics 1
set ytics 4
set xzeroaxis lt 9 lw 5
set yzeroaxis lt 9 lw 5
set style line 1 lt 1 lw 3
set style line 2 lt 3 lw 5
set style line 3 lt 10 lw 6
set style line 4 lt 12 lw 3
set style line 5 lt 9 lw 1
set grid ls 5
show grid
set xrange [-10:10]
set yrange [-10:100]
set samples 1000
set key on
f(x)= (7*x**2-28)/(sqrt(49-x**2)) 
g(x)=x**2-9
h(x)=f(x)/g(x)
i(x)=x-7
j(x)=sqrt(16-x**2)
k(x)=i(x)/j(x)
plot f(x) ls 1
# plot f(x) ls 1,g(x) ls 2, h(x) ls 3
# plot i(x) ls 1,j(x) ls 2, k(x) ls 3