Find Intervals of Increase and Decrease: y = -(x + 7/8)² - 1.2

Find the intervals of increase and decrease of the function:

y=(x+78)2115 y=-(x+\frac{7}{8})^2-1\frac{1}{5}

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1

Understand the problem

Find the intervals of increase and decrease of the function:

y=(x+78)2115 y=-(x+\frac{7}{8})^2-1\frac{1}{5}

2

Step-by-step solution

The given function is y=(x+78)2115 y = -(x+\frac{7}{8})^2 - 1\frac{1}{5} . This function is in the vertex form y=a(xh)2+k y = a(x-h)^2 + k , where a=1 a = -1 , h=78 h = -\frac{7}{8} , and k=65 k = -\frac{6}{5} .

  • The vertex of the quadratic function is (78,65)(- \frac{7}{8}, -\frac{6}{5}).
  • Since a=1 a = -1 which is less than 0, the parabola opens downward.
  • For a parabola that opens downward, the function is increasing on the interval where x<h x < h and decreasing on the interval where x>h x > h .
  • Thus, the function increasing on (,78)(- \infty, -\frac{7}{8}) and decreasing on (78,)(- \frac{7}{8}, \infty).

Therefore, the correct intervals are:
:x<78\nearrow: x < -\frac{7}{8}
:x>78\searrow: x > -\frac{7}{8}

Therefore, the final intervals of increase and decrease are:

:x>78\searrow: x > -\frac{7}{8}
:x<78\nearrow: x < -\frac{7}{8}

3

Final Answer

:x>78:x<78 \searrow:x>-\frac{7}{8}\\\nearrow:x<-\frac{7}{8}

Practice Quiz

Test your knowledge with interactive questions

Note that the graph of the function shown below does not intersect the x-axis

The parabola's vertex is A

Identify the interval where the function is decreasing:

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