identify the vertex and axis of symmetry
y=2x^2-28x+91
To identify the vertex and axis of symmetry of the quadratic equation y = 2x^2 - 28x + 91, we can use the vertex formula.
The equation of the vertex of a quadratic equation in standard form (y = ax^2 + bx + c) is given by:
x = -b / 2a
In our equation, a = 2 and b = -28.
Substituting the values into the formula, we get:
x = -(-28) / 2(2)
x = 28 / 4
x = 7
Now, to find the value of y corresponding to the x-coordinate of the vertex, we substitute the x-value (7) back into the equation:
y = 2(7^2) - 28(7) + 91
y = 2(49) - 196 + 91
y = 98 - 196 + 91
y = -7
Therefore, the vertex of the quadratic equation y = 2x^2 - 28x + 91 is (7, -7).
The axis of symmetry is a vertical line that passes through the vertex of the parabola. In this case, the equation of the axis of symmetry is x = 7.