Question

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Which of the graphs below correctly solves for x in the equation −x2 + 2x + 6 = 2x − 3?

Answer 1

$y=ax^2+bx+c\\\\\text{if a}\ \textless \ \text{0 then a parabola op}\text{ening down}\\\\\text{if a}\ \textgreater \ \text{0 then a parabola op}\text{ening up}\\\\\text{We have}\ y=-x^2+2x+6\to a=-1 \ \textless \ 0\\\text{a parabola op}\text{ening down}\to\text{the graph A and B}\\\\y=ax+b\\\\\text{if a}\ \textless \ \text{0 then a graph is decreasing}\\\text{if a}\ \textgreater \ \text{0 then a graph is increasing}\\\\\text{We have}\ y=2x-3\to a=2 \ \textgreater \ 0\\\text{a graph is increasing}\to \text{the graph B and D}\\\\\text{Therefore your answer is B}$

Answer 2

An equation is formed of two equal expressions. The correct option is B.

What is an equation?

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

To know the graph below that correctly solves for x in the equation −x²+2x+6 = 2x − 3, solve the equation formed, therefore,

−x² + 2x + 6 = 2x − 3

−x² + 2x + 6 − 2x + 3 = 0

−x² + 9  = 0

−x² = −9

x² = 9

x = ±3

Therefore,  the graphs below that correctly solve for x in the equation −x2 + 2x + 6 = 2x − 3 is the one in which the two graphs intersect when the value of x is -3 and 3.

Hence, the correct option is B.

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