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The graph of $y=2x^2-4x-4$ is shown in the $xy$ plane. Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation as written?

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Full solution

Q. The graph of

y=2x^2-4x-4

is shown in the

xy

plane. Which of the following characteristics of the graph is displayed as a constant or coefficient in the equation as written?

Equation Characteristics: The equation given is $y=2x^2-4x-4$ . The characteristics of the graph that are displayed as constants or coefficients in the equation are the leading coefficient, the linear coefficient, and the constant term.
Leading Coefficient: The leading coefficient is the coefficient of the $x^2$ term. In the equation $y=2x^2-4x-4$ , the leading coefficient is $2$ . This affects the width and the direction of the parabola. A positive leading coefficient means the parabola opens upwards.
Linear Coefficient: The linear coefficient is the coefficient of the $x$ term. In the equation $y=2x^2-4x-4$ , the linear coefficient is $-4$ . This affects the position of the vertex of the parabola along the $x$ -axis.
Constant Term: The constant term is the term without a variable. In the equation $y=2x^2-4x-4$ , the constant term is $-4$ . This affects the position of the graph along the y-axis, specifically the y-intercept of the graph.

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