Find Decreasing Intervals for y = -2x² - 8x - 10

Find the intervals where the function is decreasing:

y=2x28x10 y=-2x^2-8x-10

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the decreasing domains of the function
00:04 We'll use the formula to find the X value at the vertex
00:09 Identify the trinomial coefficients
00:13 We'll substitute appropriate values according to the given data and solve for X
00:24 This is the X value at the vertex point
00:30 The coefficient A is negative, therefore the parabola has a maximum point
00:35 From the graph we'll determine the decreasing domains of the function
00:38 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Find the intervals where the function is decreasing:

y=2x28x10 y=-2x^2-8x-10

2

Step-by-step solution

To determine where the function y=2x28x10 y = -2x^2 - 8x - 10 is decreasing, we need to find the vertex of the parabola. The vertex for a quadratic function in the form y=ax2+bx+c y = ax^2 + bx + c occurs at the x-value given by x=b2a x = -\frac{b}{2a} .

Step 1: Identify the coefficients a=2 a = -2 and b=8 b = -8 .

Step 2: Calculate the vertex x-coordinate:

x=82(2)=84=2 x = -\frac{-8}{2(-2)} = -\frac{8}{-4} = 2 .

Step 3: Since a=2 a = -2 is negative, the parabola opens downwards. Thus, the function decreases for x-values greater than x=2 x = -2 .

Therefore, the interval where the function is decreasing is x>2 x > -2 .

The correct choice is x>2 x>-2 .

3

Final Answer

x>2 x>-2

Practice Quiz

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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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