Graph the equation y, equals, minus, x, squared, minus, 4, x, plus, 5y=−x 2 −4x+5 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Sure, here are the steps to graph the equation y = -x^2 - 4x + 5:

Step 1: Identify the type of function The given equation is a quadratic function in the form y = ax^2 + bx + c, where a = -1, b = -4, and c = 5.

Step 2: Find the vertex The vertex of a parabola y = ax^2 + bx + c is given by the point (h, k), where h = -b/2a and k = c - b^2/4a. Substituting the given values, we get h = -(-4)/2*(-1) = 2 and k = 5 - (-4)^2/4*(-1) = 1. So, the vertex is (2, 1).

Step 3: Find the roots The roots of the equation can be found by setting y = 0 and solving for x. This gives us the equation -x^2 - 4x + 5 = 0. Solving this quadratic equation (either by factoring, completing the square, or using the quadratic formula), we get x = -1 and x = 5. So, the roots are (-1, 0) and (5, 0).

Step 4: Choose two more points To graph the equation, we need at least 5 points. We already have 3 points (the vertex and the roots), so we need to choose 2 more. Let's choose x = 0 and x = 3. Substituting x = 0 into the equation gives y = 5, so one point is (0, 5). Substituting x = 3 into the equation gives y = -2, so another point is (3, -2).

Step 5: Plot the points and draw the graph Plot the 5 points we found on the graph: the vertex (2, 1), the roots (-1, 0) and (5, 0), and the two additional points (0, 5) and (3, -2). Then, draw a smooth curve through the points to complete the graph of the equation.

Remember, since the coefficient of x^2 is negative, the parabola opens downwards.