Examine the following equation:

y = -2x^2 + 20x + 1

* What shape does the graph of this equation make? (Hint: You should be able to tell just by looking at the first term of the equation.)
* Does the graph open up or down (Hint: You should also be able to answer this just by looking at the first term of the equation.)

The equation describes an upside-down parabola, opening down.

Plotting the graph yourself should help you visualize the situation. Words can be confusing.

To determine the shape and direction of the graph of the given equation y = -2x^2 + 20x + 1, we can look at the coefficient of the x^2 term, which is -2.

Since the coefficient of the x^2 term is negative (-2), the graph of the equation will represent a downward-opening parabola. When the leading coefficient is negative, it indicates that the graph opens downwards.

Therefore, the graph of the equation y = -2x^2 + 20x + 1 will resemble a downward-opening parabola.