Use the graph of f (x) to find the solutions to the equation f (x) = 0.
A coordinate plane with parabola opening down. The y-intercept is 20 and the x-intercepts are 7 and negative 4.
A. two solutions: x = negative 4, 7
B. two solutions: x = 4 and negative 7
C. one solution: x = 28
D. no solutions
B. Two solutions: x = 4 and negative 7.
What are the solutions of the equation 2 x squared equals 18? Use a graph of a related function whose roots answer the question.
A. An upward facing parabola passes through points left parenthesis negative 9 comma 0 right parenthesis, left parenthesis 0 comma negative 18 right parenthesis, and left parenthesis 9 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 9
B. An upward facing parabola passes through points left parenthesis negative 3 comma 0 right parenthesis, left parenthesis 0 comma negative 9 right parenthesis, and left parenthesis 3 comma 0 right parenthesis.
There are two solutions: x equals plus or minus 3
C. An upward facing parabola passes through points left parenthesis negative 2 comma 1 right parenthesis, left parenthesis 0 comma negative 3 right parenthesis, and left parenthesis 2 comma 1 right parenthesis.
There are two solutions: x equals plus or minus start root 3 end root
D. An upward facing parabola passes through points left parenthesis negative 2 comma 13 right parenthesis, left parenthesis 0 comma 9 right parenthesis, and left parenthesis 2 comma 13 right parenthesis.
There are no solutions.
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B. An upward facing parabola passes through points left parenthesis negative 3 comma 0 right parenthesis, left parenthesis 0 comma negative 9 right parenthesis, and left parenthesis 3 comma 0 right parenthesis. There are two solutions: x equals plus or minus 3.
To find the solutions to the equation f(x) = 0 using the graph of f(x), we need to identify the x-values where the graph intersects the x-axis.
Looking at the given graph, we see that the parabola opens downwards and has x-intercepts at 7 and -4. The y-intercept is at (0, 20).
In order for f(x) to be equal to zero, the graph must cross the x-axis. Thus, the solutions to the equation f(x) = 0 are the x-values where the graph intersects the x-axis.
From the graph, it is clear that the x-intercepts are -4 and 7. Therefore, the solutions to the equation f(x) = 0 are x = -4 and x = 7.
So, the correct answer is Option A: two solutions: x = -4, 7.