Function: y=x2+5x−7𝑦=𝑥2+5𝑥−7Vertex: (( ,, ))Solutions: (( , )) and (( ,, ))CheckQuestion 3

The function given is a quadratic function in the form y = ax^2 + bx + c.

Step 1: Identify the coefficients a, b, and c in the equation. Here, a = 1, b = 5, and c = -7.

Step 2: Find 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 -5/(2*1) = -5/2 = -2.5.

Step 3: Substitute x = -2.5 in the equation to find the y-coordinate of the vertex. y = (-2.5)^2 + 5*(-2.5) - 7 = 6.25 - 12.5 - 7 = -13.25. So, the vertex of the parabola is (-2.5, -13.25).

Step 4: Find the solutions of the equation. The solutions are the x-values for which y = 0. This can be found by solving the equation x^2 + 5x - 7 = 0. This is a quadratic equation and 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 = [-5 ± sqrt((5)^2 - 41(-7))] / (2*1) = [-5 ± sqrt(25 + 28)] / 2 = [-5 ± sqrt(53)] / 2. So, the solutions of the equation are x = [-5 + sqrt(53)] / 2 and x = [-5 - sqrt(53)] / 2.