identify the vertex and axis of symmetry
y=2x^2-28x+91
To identify the vertex and axis of symmetry of the quadratic function y = 2x^2 - 28x + 91, we need to convert the quadratic equation to vertex form, which is given by the formula y = a(x - h)^2 + k, where (h, k) represents the coordinates of the vertex.
Step 1: Identify the coefficient values
In the given equation, we have a = 2, b = -28, and c = 91.
Step 2: Find the x-coordinate of the vertex
The x-coordinate of the vertex can be found using the formula x = -b / (2a). Plugging in the values, we get:
x = -(-28) / (2 * 2) = 28 / 4 = 7
Step 3: Substitute the x-coordinate into the equation to find the y-coordinate
Using the x-coordinate we found in the previous step, we substitute x = 7 into the original equation:
y = 2(7)^2 - 28(7) + 91
y = 2(49) - 196 + 91
y = 98 - 196 + 91
y = -7
So, the coordinates of the vertex are (7, -7).
Step 4: Identify the axis of symmetry
The axis of symmetry is given by the equation x = h, where h represents the x-coordinate of the vertex. In this case, the axis of symmetry is x = 7.
Therefore, the vertex of the quadratic function is (7, -7), and the axis of symmetry is x = 7.