Instructions: Use a graphing calculator to approximate the zeros and vertex of the following quadratic functions. Round to one decimal place, if necessary. Fill in solutions least to greatest (left to right).y=−x2−4x+7

Step 1: Identify the coefficients from the equation y = -x^2 - 4x + 7. Here, a = -1, b = -4, and c = 7.

Step 2: Calculate the vertex of the parabola. The x-coordinate of the vertex can be found using the formula -b/2a. Substituting the values of a and b, we get -(-4)/2*(-1) = 2. The y-coordinate of the vertex can be found by substituting the x-coordinate into the equation, so y = -(2)^2 - 4*2 + 7 = -4 - 8 + 7 = -5. So, the vertex of the parabola is (2, -5).

Step 3: To find the zeros of the function, set y = 0 and solve for x. So, 0 = -x^2 - 4x + 7. This can be solved using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / 2a. Substituting the values of a, b, and c, we get x = [4 ± sqrt((-4)^2 - 4*(-1)7)] / 2(-1) = [4 ± sqrt(16 + 28)] / -2 = [4 ± sqrt(44)] / -2.

Step 4: Simplify to get the two solutions. x = [4 ± sqrt(44)] / -2 = -2 ± sqrt(11). So, the zeros of the function are -2 - sqrt(11) and -2 + sqrt(11).

Step 5: Use a graphing calculator to approximate these values. -2 - sqrt(11) is approximately -5.3 and -2 + sqrt(11) is approximately 1.3.

So, the zeros of the function are approximately -5.3 and 1.3, and the vertex is (2, -5).