Graph the equation y=-x^2+14x-48 on the accompanying set of axes . You must plot 5 points including the roots and the vertex. Using the graph, determine the roots of the equation -x^2+14x-48=0 Click to plot points.Click points to delete them.

To graph the equation and find the roots, we will follow these steps:Step 1: Find the roots of the equation.The roots are the values of for which . To find the roots, we set the equation equal to zero and solve for : We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. The quadratic formula is: For our equation, , , and . Plugging these values into the quadratic formula gives us: So the roots are: The roots are and .Step 2: Find the vertex of the parabola.The vertex form of a parabola is \(y = a(x - h)^2 + k\), where \((h, k)\) is the vertex of the parabola. For a parabola in the form , the x-coordinate of the vertex is given by . In our case: To find the y-coordinate of the vertex, we substitute into the original equation: So the vertex of the parabola is \((7, 1)\).Step 3: Plot the roots and the vertex.On the Cartesian coordinate system, plot the points \((6, 0)\), \((8, 0)\), and \((7, 1)\).Step 4: Choose two additional points to plot.To graph the parabola accurately, we need at least two more points. Let's choose and and calculate the corresponding y-values:For : For : Plot the points \((5, -3)\) and \((9, -3)\) on the graph.Step 5: Draw the parabola.Connect the points with a smooth curve to form the parabola, making sure it opens downward (since the coefficient of is negative).Answer:The roots of the equation are and , as determined by the points where the parabola crosses the x-axis on the graph.