Question
Determine the vertex and axis of symmetry of y = x^2 - 10x + 3
Answers
GPT 3.5
To find the vertex and axis of symmetry of the quadratic function y = x^2 - 10x + 3, we can use the formula:
x = -b/2a
In this equation, a = 1, b = -10, and c = 3.
Plugging these values into the formula, we get:
x = -(-10) / 2(1)
x = 10 / 2
x = 5
So, the x-coordinate of the vertex is 5.
To find the y-coordinate of the vertex, we substitute this value of x back into the equation:
y = (5)^2 - 10(5) + 3
y = 25 - 50 + 3
y = -22
So, the vertex is (5, -22).
The axis of symmetry is the vertical line that passes through the vertex. Since the x-coordinate of the vertex is 5, the equation of the axis of symmetry is x = 5.
x = -b/2a
In this equation, a = 1, b = -10, and c = 3.
Plugging these values into the formula, we get:
x = -(-10) / 2(1)
x = 10 / 2
x = 5
So, the x-coordinate of the vertex is 5.
To find the y-coordinate of the vertex, we substitute this value of x back into the equation:
y = (5)^2 - 10(5) + 3
y = 25 - 50 + 3
y = -22
So, the vertex is (5, -22).
The axis of symmetry is the vertical line that passes through the vertex. Since the x-coordinate of the vertex is 5, the equation of the axis of symmetry is x = 5.