Answer:
I'm unable to plot graph, but I can give you the steps to graph the equation y = -²- 10x - 16 on the given set of axes.
Plot the vertex of the parabola: The vertex of the parabola is the point where the parabola changes direction. To find the vertex, you can use the formula (-b/2a, f(-b/2a)), where a, b, and c are the coefficients of the equation y = ax² + bx + c. In this case, a = -1, b = -10, and c = -16, so the vertex is (-10/2(-1), -(-10/2(-1))² - 10(-10/2(-1)) - 16) = (5,16).
Plot the roots: The roots of the equation are the values of x that make y = 0. To find the roots, you can set y = 0 and solve for x. In this case, y = 0 = -x² - 10x - 16. This equation can be solved by factoring or by using the quadratic formula. The roots are x = 4 and x = -2.
Plot five points on the parabola, including the vertex and the roots. To do this, you can substitute different values of x into the equation y = -x² - 10x - 16 and find the corresponding y-values. For example, you could plot the point (4,0), which is one of the roots, and (5,16), which is the vertex.
Connect the points to form a parabola.
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Explanation: