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A parabola has an equation, [m]y = 2x^2 - 5x + c [/m] and passes

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KarunMendiratta
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A parabola has an equation, [m]y = 2x^2 - 5x + c [/m] and passes [#permalink] New post   04 Mar 2021, 11:24
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A parabola has an equation, \(y = 2x^2 - 5x + c \) and passes through \((2,5)\)

Quantity A
Quantity B
y-coordinate of the vertex
\(c\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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KarunMendiratta
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Re: A parabola has an equation, [m]y = 2x^2 - 5x + c [/m] and passes [#permalink] New post   05 Mar 2021, 08:07
KarunMendiratta wrote:
A parabola has an equation, \(y = 2x^2 - 5x + c \) and passes through \((2,5)\)

Quantity A
Quantity B
y-coordinate of the vertex
\(c\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


OA Explanation:

Plug in \(x = 2\) and \(y = 5\) in the equation;

\(5 = 2(2)^2 - 5(2) + c\)
\(c = 7\)

In Parabola with equation: y = ax^2 + bx + c
x-coordinate of the Vertex = \(\frac{-b}{2a} = \frac{-(-5)}{2(2)} = \frac{5}{4}\)
y-coordinate of the vertex = \(2(\frac{5}{4})^2 -5(\frac{5}{4}) + 7 = 3.875\)

Col. A: \(3.875\)
Col. B: \(7\)

Hence, option B
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Re: A parabola has an equation, [m]y = 2x^2 - 5x + c [/m] and passes [#permalink]
05 Mar 2021, 08:07
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