what point is symmetrical to (-1,-3) for the graph of y=x^2+12x+8?
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To find the point symmetric to (-1, -3), we need to find the x-coordinate of the point.
The formula for finding the x-coordinate of the point symmetric to a given point (h, k) is given by the equation x = 2h - x1, where x1 is the x-coordinate of the given point.
In this case, h = -1 and x1 = -1.
So, the x-coordinate of the point symmetric to (-1, -3) is x = 2*(-1) - (-1) = -2 + 1 = -1.
To find the y-coordinate of the symmetric point, we substitute the x-coordinate into the equation of the graph:
y = (-1)^2 + 12*(-1) + 8
= 1 - 12 + 8
= -3.
Therefore, the point symmetric to (-1, -3) for the graph of y = x^2 + 12x + 8 is (-1, -3).
That's not right
Apologies for the incorrect response. Let's try to find the correct answer.
The equation of the graph is y = x^2 + 12x + 8.
To find the point symmetric to (-1, -3), we need to find the point reflected across the axis of symmetry. For any quadratic equation in the form y = ax^2 + bx + c, the axis of symmetry is given by the equation x = -b/2a.
In this case, a = 1 and b = 12. Thus, the axis of symmetry is x = -12/(2*1) = -6.
The point symmetric to (-1, -3) is located on the same vertical line as the axis of symmetry, but in the opposite direction. Therefore, the x-coordinate of the symmetric point is -6 - (-1) = -6 + 1 = -5.
Now we substitute the x-coordinate (-5) into the equation y = x^2 + 12x + 8:
y = (-5)^2 + 12(-5) + 8
= 25 - 60 + 8
= -27.
Thus, the point symmetric to (-1, -3) for the graph of y = x^2 + 12x + 8 is (-5, -27).
wrong
Apologies for the mistake. Let's try again to find the correct answer.
To find the point symmetric to (-1, -3) for the graph of y = x^2 + 12x + 8, we need to find the corresponding y-coordinate.
Let's call the symmetric point (a, b). Since it is symmetric to (-1, -3), the x-coordinate of the symmetric point will be the same as the x-coordinate of (-1, -3), which is -1. Therefore, a = -1.
To find the y-coordinate, we substitute a = -1 into the equation y = x^2 + 12x + 8:
b = (-1)^2 + 12(-1) + 8
= 1 - 12 + 8
= -3.
Therefore, the point symmetric to (-1, -3) for the graph of y = x^2 + 12x + 8 is (-1, -3).
that's not right.
Apologies for the confusion. Let's try again using the correct approach.
To find the point symmetric to (-1, -3) for the graph of y = x^2 + 12x + 8, we need to find the reflection of (-1, -3) across the axis of symmetry.
The axis of symmetry is given by the equation x = -b/2a, where a and b are the coefficients of the quadratic equation.
In this case, a = 1 and b = 12, so the axis of symmetry is given by x = -12/2(1) = -6.
The x-coordinate of the symmetric point will be the same as the x-coordinate of (-1, -3), which is -1.
Since the axis of symmetry passes through the midpoint between the point and its reflection, the distance from -6 to -1 is the same as the distance from -1 to the symmetric point.
Thus, the x-coordinate of the symmetric point is -6 + (-1) = -7.
To find the y-coordinate, we substitute x = -7 into the equation y = x^2 + 12x + 8:
y = (-7)^2 + 12(-7) + 8
= 49 - 84 + 8
= -27.
Therefore, the point symmetric to (-1, -3) for the graph of y = x^2 + 12x + 8 is (-7, -27).