Question
Determine the vertex and axis of symmetry of y=x2−10x+3 .(1 point) vertex: (); axis of symmetry: x=
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GPT 3.5
To determine the vertex and axis of symmetry of the given quadratic function, we can use the formula:
x = -b/2a
where a, b, and c are the coefficients of the quadratic equation in the general form ax^2 + bx + c.
In this case, the quadratic equation is y = x^2 - 10x + 3, where:
a = 1
b = -10
c = 3
The vertex x-coordinate can be found using the formula x = -b/2a:
x = -(-10)/2(1) = 10/2 = 5
To find the y-coordinate of the vertex, substitute the x-coordinate into the equation:
y = (5)^2 - 10(5) + 3 = 25 - 50 + 3 = -22
Therefore, 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
where a, b, and c are the coefficients of the quadratic equation in the general form ax^2 + bx + c.
In this case, the quadratic equation is y = x^2 - 10x + 3, where:
a = 1
b = -10
c = 3
The vertex x-coordinate can be found using the formula x = -b/2a:
x = -(-10)/2(1) = 10/2 = 5
To find the y-coordinate of the vertex, substitute the x-coordinate into the equation:
y = (5)^2 - 10(5) + 3 = 25 - 50 + 3 = -22
Therefore, 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.
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