graph A
no x-intercept
no y-intercept
H.A is y = 5
V. A. is x = 0
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Answer: [tex]\frac{150}{31}[/tex]
Step by step explanation:
log₆(5x + 6) - log₆(x - 4) = 2
log₆[tex](\frac{5x+6}{x-4})[/tex] = 2
[tex](\frac{5x+6}{x-4})[/tex] = 6²
[tex](\frac{5x+6}{x-4})[/tex] = 36
5x + 6 = 36(x - 4)
5x + 6 = 36x - 144
6 = 31x - 144
150 = 31x
[tex]\frac{150}{31}[/tex] = x
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Answers:
- a. (-1, -5)
- b. up
- c. x = -1
- d. [tex]\frac{-2+\sqrt{15}}{3} and\frac{-2-\sqrt{15}}{3}[/tex]
- e. -2
- f. see attachment
- g. domain (-∞, ∞) range [-5, ∞)
Explanation:
f(x) = 3x² + 6x - 2
a=3 b=6 c=-2
x = [tex]\frac{-b}{2a} =\frac{-6}{2(3)} = \frac{-6}{6} = -1[/tex]
Axis Of Symmetry: x = -1
f(-1) = 3(-1)² + 6(-1) - 2
= 3 - 6 - 2
= -5
Vertex: (-1, -5)
x = [tex]\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}[/tex]
= [tex]\frac{-6+/-\sqrt{6^{2}-4(3)(-2)}}{2(3)}[/tex]
= [tex]\frac{-6+/-\sqrt{36+24}}{6}[/tex]
= [tex]\frac{-6+/-\sqrt{60}}{6}[/tex]
= [tex]\frac{-6+/-2\sqrt{15}}{6}[/tex]
= [tex]\frac{-2+/-\sqrt{15}}{3}[/tex]
x-intercepts: [tex]\frac{-2+/-\sqrt{15}}{3}[/tex]
