Use this function for problems 1 - 10: y = (x - 2) - 121) Give the coordinates of the vertex of the graph.2) Convert the function to standard form. 4) Convert the function to factored form.3) Give the coordinates of the y-intercept. 5) Give the coordinates of the x-intercepts.6) Graph the function labeling the vertex, y-intercept, and x-intercepts.7) Enter the function on your calculator in vertex form and graph it. How does it compare to your graph?8) Enter the function on your calculator in standard form and graph it. How does it compare to your graph?9) Enter the function on your calculator in factored form and graph it. How does it compare to your graph?10) Use your calculator to find the vertex, x-intercepts, and y-intercept. Do they match yours

1. The vertex of the graph is given by the point (h, k) where h is the value of x that makes the derivative of the function zero and k is the value of the function at h. In this case, the function is already in vertex form y = a(x - h)^2 + k, where a is the coefficient of the square term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex. So, the vertex is (2, -121).

2. The standard form of a quadratic function is y = ax^2 + bx + c. To convert the function to standard form, expand the square term: y = (x^2 - 4x + 4) - 121 = x^2 - 4x - 117.

3. The y-intercept is the value of the function when x = 0. Substituting x = 0 into the function gives y = (0 - 2)^2 - 121 = -117. So, the y-intercept is (0, -117).

4. The factored form of a quadratic function is y = a(x - r)(x - s), where r and s are the roots of the equation. To find the roots, set the function equal to zero and solve for x: 0 = x^2 - 4x - 117. Using the quadratic formula gives x = 2 ± sqrt(121), so the factored form is y = (x - (2 + sqrt(121)))(x - (2 - sqrt(121))).

5. The x-intercepts are the values of x that make the function zero. These are the same as the roots found in step 4, so the x-intercepts are (2 + sqrt(121), 0) and (2 - sqrt(121), 0).

6. To graph the function, plot the vertex, y-intercept, and x-intercepts found in the previous steps, and draw a parabola through these points. The parabola opens upwards because the coefficient of the square term is positive.

7-10) These steps involve using a calculator to graph the function and compare the results with the previous steps. The results should match the calculations made in steps 1-5.