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 \(y = -x^2 + 14x - 48\) and find the roots, we will follow these steps:Step 1: Find the roots of the equation.The roots are the values of \(x\) for which \(y = 0\). To find the roots, we set the equation equal to zero and solve for \(x\):\[-x^2 + 14x - 48 = 0\]We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. The quadratic formula is:\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]For our equation, \(a = -1\), \(b = 14\), and \(c = -48\). Plugging these values into the quadratic formula gives us:\[x = \frac{-14 \pm \sqrt{14^2 - 4(-1)(-48)}}{2(-1)}\]\[x = \frac{-14 \pm \sqrt{196 - 192}}{-2}\]\[x = \frac{-14 \pm \sqrt{4}}{-2}\]\[x = \frac{-14 \pm 2}{-2}\]So the roots are:\[x = \frac{-14 + 2}{-2} = \frac{-12}{-2} = 6\]\[x = \frac{-14 - 2}{-2} = \frac{-16}{-2} = 8\]The roots are \(x = 6\) and \(x = 8\).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 \(y = ax^2 + bx + c\), the x-coordinate of the vertex is given by \(h = -\frac{b}{2a}\). In our case:\[h = -\frac{14}{2(-1)} = 7\]To find the y-coordinate of the vertex, we substitute \(x = 7\) into the original equation:\[y = -(7)^2 + 14(7) - 48\]\[y = -49 + 98 - 48\]\[y = 1\]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 \(x = 5\) and \(x = 9\) and calculate the corresponding y-values:For \(x = 5\):\[y = -(5)^2 + 14(5) - 48\]\[y = -25 + 70 - 48\]\[y = -3\]For \(x = 9\):\[y = -(9)^2 + 14(9) - 48\]\[y = -81 + 126 - 48\]\[y = -3\]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 \(x^2\) is negative).Answer:The roots of the equation \(-x^2 + 14x - 48 = 0\) are \(x = 6\) and \(x = 8\), as determined by the points where the parabola crosses the x-axis on the graph.