A parabola ,f, intersect the x axis at A and B and the y axis at C. The axis of symmetry of the parabola has the equation x=-3.The line through A and C has the equation g(x)=x+7. Determine the coordinates of A,B and C
(x+3)^2 = p (y-q)
g = x + 7
when g = 0, x = A
0 = A + 7
A = -7
so A is 4 to the left of -3
therefore B is 4 to the right of -3 or at B = +1
so
g = 7 at x = 0 so C = 7
A = (-7,0)
B = (1,0)
C = (0,7)
To determine the coordinates of points A, B, and C, we need to use the given information about the parabola and the equation of the line.
1. Axis of Symmetry: The equation of the axis of symmetry of a parabola is given by x = -h, where (h, k) is the vertex of the parabola. In this case, x = -3 is the equation of the axis of symmetry.
2. Vertex: The vertex of the parabola lies on the axis of symmetry. Since we know that the axis of symmetry is x = -3, the x-coordinate of the vertex is -3.
3. x-intercepts: A parabola intersects the x-axis at the points where y = 0. To find the x-intercepts, we set y = 0 in the equation of the parabola.
4. y-intercept: A parabola intersects the y-axis at the point where x = 0. To find the y-intercept, we set x = 0 in the equation of the parabola.
Using this information, let's solve for the coordinates of points A, B, and C:
1. Axis of symmetry: x = -3
2. Vertex: The x-coordinate of the vertex is -3. Since the axis of symmetry is x = -3, the vertex is (-3, k).
3. x-intercepts: Set y = 0 in the equation of the parabola to find the x-intercepts:
Substitute y = 0 into the equation of the parabola and solve for x.
4. y-intercept: Set x = 0 in the equation of the parabola to find the y-intercept:
Substitute x = 0 into the equation of the parabola and solve for y.
5. Line equation and point A: The equation of the line g(x) = x + 7 passes through points A and C. We need to find the x-coordinate of point A to determine its coordinates.
Now let's plug in the information and solve for the coordinates of A, B, and C.