Solve the equation graphically to four decimal places.
-Let f(x) = -0.5x2 + 4x + 2, find f(x) = -5.
A) No solution
B) 9.4772
C) -1.4772
D) -1.4772, 9.4772

Question

Quizplus · Accepted Answer

To solve graphically, we need to plot the graph of f(x) = -0.5x² + 4x + 2, and find the x-coordinates where the graph intersects the line y = -5. So, we will create the graph and plot the line y = -5 on the same graph to find the intersection point(s).
We can see that the graph of f(x) is a parabola that opens downward, and its vertex is at (4,6). We can plot a few points to sketch the graph more accurately. 
Now, we plot the line y = -5 on the same graph by drawing a horizontal line at y = -5. 
We can see that the line intersects the graph of f(x) at two points, which are symmetric about the vertical line x = 4 (the axis of symmetry of the parabola).
Using a ruler or other tools, we can estimate the x-coordinates of these intersection points as approximately -1.4772 and 9.4772.
Therefore, the solutions to f(x) = -5 are x = -1.4772 and x = 9.4772, so the answer is D. To solve the equation graphically, we need to plot the graph of y = f(x) and the horizontal line y = -5 on the same graph and find their intersection points.

Firstly, let's plot the graph of y = f(x):

We can see that the graph is a parabola that opens downwards, its vertex is at (4,4), and it intersects the x-axis at x = 2 and x = 8.

Now, let's plot the horizontal line y = -5:

We can see that the line intersects the y-axis at y = -5.

Next, we need to find the intersection points of the graph of y = f(x) and the horizontal line y = -5:

We can see that there are two intersection points: one at x = -1.4772 and the other at x = 9.4772.

Therefore, the solutions to the equation f(x) = -5 are x = -1.4772 and x = 9.4772, and the correct answer is D.

Solve the Equation Graphically to Four Decimal Places