What point is symmetrical to (3,−9)
for the graph of y=x2−12x+18
?(1 point)
Responses
(−3,−9)
left parenthesis negative 3 comma negative 9 right parenthesis
(9,−9)
left parenthesis 9 comma negative 9 right parenthesis
(3,9)
left parenthesis 3 comma 9 right parenthesis
(−9,3)
To find the point that is symmetrical to (3,-9) for the graph of y=x^2-12x+18, we can use the formula for the axis of symmetry. The formula for the axis of symmetry is x=-b/2a, where a and b are the coefficients of the quadratic equation (in this case, a=1 and b=-12).
Substituting the values into the formula, we get x=-(-12)/2(1) = 12/2 = 6.
Since the point (3,-9) is to the left of the axis of symmetry, the symmetrical point will be to the right. Therefore, the symmetrical point is (9,-9).
To find the point that is symmetrical to (3,-9) for the graph of y=x^2-12x+18, you need to find the reflection of the given point across the axis of symmetry. The axis of symmetry for a quadratic function of the form y=ax^2+bx+c can be found using the formula x = -b/2a.
In this case, the quadratic function is y = x^2 - 12x + 18. To find the axis of symmetry, we need to find the value of x when y is at its maximum or minimum point. For a quadratic function with a positive coefficient of x^2 (a>0), the maximum or minimum point will be the vertex of the parabola.
The vertex can be found using the formula x = -b/2a. In this case, a=1 and b=-12. Plugging these values into the formula, we get:
x = -(-12)/(2*1)
x = 12/2
x = 6
Therefore, the axis of symmetry is x = 6.
To find the point that is symmetrical to (3,-9), we need to find the reflection of the x-coordinate across the axis of symmetry (x=6). The reflection can be found using the formula:
reflected_x = 2*axis_of_symmetry_x - given_x
Substituting the values, we get:
reflected_x = 2*6 - 3
reflected_x = 12 - 3
reflected_x = 9
Therefore, the x-coordinate of the point that is symmetrical to (3,-9) is 9. The y-coordinate remains the same.
Hence, the point that is symmetrical to (3,-9) for the graph of y=x^2-12x+18 is (9,-9).
To find the point that is symmetrical to (3, -9) for the graph of y = x^2 - 12x + 18, we need to find the reflection of the point (3, -9) across the axis of symmetry. The axis of symmetry for a quadratic function in the form y = ax^2 + bx + c is given by the equation x = -b/2a.
In this case, the equation is y = x^2 - 12x + 18, so the coefficients are a = 1 and b = -12. Plugging these values into the equation x = -b/2a, we get:
x = -(-12) / (2 * 1) = 12 / 2 = 6
So, the axis of symmetry is x = 6. To find the point that is symmetrical to (3, -9), we need to reflect the x-coordinate across the axis of symmetry. Since the x-coordinate of (3, -9) is 3, the distance between 3 and 6 is 6 - 3 = 3. Therefore, the reflected x-coordinate will be 6 + 3 = 9.
The y-coordinate will remain the same for the point that is symmetrical to (3, -9). So, the point that is symmetrical to (3, -9) for the given graph is (9, -9).
Hence, the correct answer is: (9, -9).