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Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Medium

$y = x^{2} + 1.7$

$y = 1.7 - x$

Which graph represents the given system of equations?

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Explanation

Choice A is correct. The graph of a quadratic equation in the form $y = x^{2} + c$ has its vertex at $left parenthesis 0 comma c right parenthesis$ . The first equation in the given system of equations is $y = x^{2} + 1.7$ , so the graph of this quadratic equation has its vertex at $left parenthesis 0 comma 1.7 right parenthesis$ . The graph of a linear equation of the form $y = b - x$ has a slope of $negative 1$ and a y-intercept at $left parenthesis 0 comma b right parenthesis$ . The second equation in the given system of equations is $y = 1.7 - x$ , so the graph of this linear equation has a slope of $negative 1$ and a y-intercept at $left parenthesis 0 comma 1.7 right parenthesis$ . Of the choices, only choice A has the graph of a quadratic equation with its vertex at $left parenthesis 0 comma 1.7 right parenthesis$ and the graph of a linear equation with a slope of $negative 1$ and a y-intercept at $left parenthesis 0 comma 1.7 right parenthesis$ .

Choice B is incorrect. This graph represents a system in which the second equation is $y = 1.7 + x$ , not $y = 1.7 - x$ .

Choice C is incorrect. This graph represents a system in which the first equation is $y = (x + 1.7)^{2}$ , not $y = x^{2} + 1.7$ .

Choice D is incorrect. This graph represents a system in which the first equation is $y = (x + 1.7)^{2}$ , not $y = x^{2} + 1.7$ , and the second equation is $y = 1.7 + x$ , not $y = 1.7 - x$ .