Advanced Algebra Final Exam
1.
What is the vertex of the parabola
f(x)=3
x
2
+
2
3
x−7
MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacIcacaWG4bGaaiykaiabg2da9iaaiodacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSYaaSqaaSqaaiaaikdaaeaacaaIZaaaaOGaamiEaiabgkHiTiaaiEdaaaa@420E@
?
2.
Sketch the graph of the function
g(x)=−
(
1
2
)
x
+4
MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4zaiaacIcacaWG4bGaaiykaiabg2da9iabgkHiTmaabmaabaWaaSaaaeaacaaIXaaabaGaaGOmaaaaaiaawIcacaGLPaaadaahaaWcbeqaaiaadIhaaaGccqGHRaWkcaaI0aaaaa@4107@
.
3. Solve
by completing the square:
2
x
2
−8x+3=0
MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHsislcaaI4aGaamiEaiabgUcaRiaaiodacqGH9aqpcaaIWaaaaa@3EA5@
4. Sketch
the graph of the inequality:
y≥−
x
2
+6x−7
MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabgwMiZkabgkHiTiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaaI2aGaamiEaiabgkHiTiaaiEdaaaa@3FDC@
5. Simplify:
a.
(
x
2
y
y
−4
)
2
⋅ (
x
0
y
−6
y
2
)
MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaadaWcaaqaaiaadIhadaahaaWcbeqaaiaaikdaaaGccaWG5baabaGaamyEamaaCaaaleqabaGaeyOeI0IaaGinaaaaaaaakiaawIcacaGLPaaadaahaaWcbeqaaiaaikdaaaGccqGHflY1caaMc8UaaGPaVlaaykW7daqadaqaamaalaaabaGaamiEamaaCaaaleqabaGaaGimaaaakiaadMhadaahaaWcbeqaaiabgkHiTiaaiAdaaaaakeaacaWG5bWaaWbaaSqabeaacaaIYaaaaaaaaOGaayjkaiaawMcaaaaa@4D8D@
b.
2
3/4
⋅
2
1/2
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c.
27
x
3
3
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6.
Find the points of intersection of the graphs of
x
2
+
y
2
=8
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and
y=
1
2
x+1
MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2da9maalaaabaGaaGymaaqaaiaaikdaaaGaamiEaiabgUcaRiaaigdaaaa@3C13@
7. Condense
and evaluate:
log
4
24−
log
4
6
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.
8. Solve
for x:
(
3−
2
x+1
)
(
3+
3
x
)
=2
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9. Find
the vertices:
(x−3)
2
12
+
(y−2)
2
16
=1
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10. Write the
formula for the nth term of the
sequence:
1
2
, 2,
7
2
, 5,
13
2
, …
MathType@MTEF@5@5@+=feaafiart1ev1aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSqaaSqaaiaaigdaaeaacaaIYaaaaOGaaiilaiaaykW7caaMc8UaaGOmaiaacYcacaaMc8UaaGPaVpaaleaaleaacaaI3aaabaGaaGOmaaaakiaacYcacaaMc8UaaGPaVlaaiwdacaGGSaGaaGPaVlaaykW7daWcbaWcbaGaaGymaiaaiodaaeaacaaIYaaaaOGaaiilaiaaykW7caaMc8UaeSOjGSeaaa@5103@
.
11. Find the
sum:
∑
n=1
∞
1
4
(
1
2
)
n−1
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