Graph y=-1/2x^2-5x-12

Math
Combine and .
Find the properties of the given parabola.
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Rewrite the equation in vertex form.
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Complete the square for .
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Use the form , to find the values of , , and .
Consider the vertex form of a parabola.
Substitute the values of and into the formula .
Simplify the right side.
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Simplify the denominator.
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Multiply by .
Combine and .
Simplify the expression.
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Divide by .
Divide by .
Multiply by .
Find the value of using the formula .
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Simplify each term.
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Raise to the power of .
Simplify the denominator.
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Multiply by .
Combine and .
Divide by .
Move the negative in front of the fraction.
Multiply .
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Multiply by .
Multiply by .
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Add and .
Substitute the values of , , and into the vertex form .
Set equal to the new right side.
Use the vertex form, , to determine the values of , , and .
Since the value of is negative, the parabola opens down.
Opens Down
Find the vertex .
Find , the distance from the vertex to the focus.
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Find the distance from the vertex to a focus of the parabola by using the following formula.
Substitute the value of into the formula.
Simplify.
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Cancel the common factor of and .
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Rewrite as .
Move the negative in front of the fraction.
Combine and .
Divide by .
Find the focus.
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The focus of a parabola can be found by adding to the y-coordinate if the parabola opens up or down.
Substitute the known values of , , and into the formula and simplify.
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
Find the directrix.
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The directrix of a parabola is the horizontal line found by subtracting from the y-coordinate of the vertex if the parabola opens up or down.
Substitute the known values of and into the formula and simplify.
Use the properties of the parabola to analyze and graph the parabola.
Direction: Opens Down
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Direction: Opens Down
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Select a few values, and plug them into the equation to find the corresponding values. The values should be selected around the vertex.
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Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Divide by .
Multiply by .
Multiply by .
Simplify by adding and subtracting.
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Add and .
Subtract from .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Multiply by .
Find the common denominator.
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Write as a fraction with denominator .
Multiply by .
Multiply and .
Write as a fraction with denominator .
Multiply by .
Multiply and .
Combine the numerators over the common denominator.
Simplify each term.
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Multiply by .
Multiply by .
Simplify the expression.
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Add and .
Subtract from .
Move the negative in front of the fraction.
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Raise to the power of .
Divide by .
Multiply by .
Multiply by .
Simplify by adding and subtracting.
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Add and .
Subtract from .
The final answer is .
The value at is .
Replace the variable with in the expression.
Simplify the result.
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Simplify each term.
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Cancel the common factor of and .
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Rewrite as .
Apply the product rule to .
Raise to the power of .
Multiply by .
Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Multiply by .
Multiply by .
Simplify by adding and subtracting.
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Add and .
Subtract from .
The final answer is .
The value at is .
Graph the parabola using its properties and the selected points.
Graph the parabola using its properties and the selected points.
Direction: Opens Down
Vertex:
Focus:
Axis of Symmetry:
Directrix:
Graph y=-1/2x^2-5x-12

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