A parabola has the equation y=x/2-x+6
(A) find the y-intercept
(B) find the x-intercept
(C) Find the coordinates of the turning point
(D) sketch the parabola shows the coordinates of the turning point and the intercept
learn to type math! x/2 - x + 6 is not a parabola!
y = x^2-x+6
(A) when x=0, y=6
(B) there are no x-intercepts, since the discriminant is negative
(C) the vertex is at (1/2,23/4)
A) The y-intercept is where the parabola intersects with the y-axis. To find it, we set x=0 in the equation and solve for y:
y = (0)/2 - (0) + 6 = 6
Therefore, the y-intercept is (0, 6).
B) The x-intercepts are where the parabola intersects with the x-axis. To find them, we set y=0 in the equation and solve for x:
0 = x/2 - x + 6
0 = -x/2 + 6
-6 = -x/2
x = 12
Therefore, the x-intercept is (12, 0).
C) The turning point of the parabola is located at the vertex, which is at the center of symmetry. To find it, we can complete the square:
y = x/2 - x + 6
y = 1/2(x - 2)^2 + 2
Therefore, the turning point is at (2, 2).
D) To sketch the parabola, we can use the information we found above. The y-intercept is (0, 6) and the x-intercept is (12, 0). The turning point is at (2, 2).
Here is the sketch of the parabola:
