Vertex of a Quadratic Equation Practice

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Question 1

Find the coordinates of the vertex of y = -3x2 -6x + 2.

Answer

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Select and check your answer...

A. (-2,3)
B. (2,-3)
C. (-1,5)
D. (1,-5)

Step by Step Solution

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    Step 1

    We can start with the formula for the x-coordinate of the vertex of the quadratic equation:

    formula for the x-coordinate of the vertex, x= -b/2a

    Where a and b are the coefficients in the general quadratic equation shown below:

    general quadratic equation, y = ax^2+bx+c
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    Step 2

    Next, to find the values of a and b, we can compare the quadratic equation with the general quadratic equation as shown:

    Comparing the equations

    By comparing, we have a = -3, b = -6 and c = 2

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    Step 3

    Now, we can substitute the equation with span class="bold text-gold">a = -3 and b = -6. By doing so, we can solve for x.

    solving for x and it is found to be -1
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    Step 4

    Hence, we have:

    x-coordinate of the vertex, x = -1
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    Step 5

    With x = -1, we can use it to find the y-coordinate of the vertex. To do so, we substitute x = -1 into the equation as shown below:

    y-coordinate of the vertex is 5
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    Step 6

    The y-coordinate of the vertex is 5. Therefore the coordinates of the vertex is (-1,5).

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    Step 7

    Clearly, the answer is C.