Answer:
yes
yes
no
no
yes
Step-by-step explanation:
f(x) = y = x² + 2x = x(x + 2)
the y-intercept (the point with the y value where x = 0) is
y = 0² + 2×0 = 0
yes, the y-intercept is (0, 0).
yes, the graph opens upward, as x² is the most powerful and therefore driving term in the expression. so, it behaves basically like x².
no, the x-intercepts are the points, where y = 0.
and while (0, 0) is correct, but (2, 0) is not.
x = 2 gives us 2² + 2×2 = 4 + 4 = 8 as y value.
the second correct x-intercept would be (-2, 0).
x = -2 gives us (-2)² + 2×-2 = 4 - 4 = 0
no (see last point)
yes, the vertex is (-1, -1).
we get the extreme value (in this case the minimum, as the curve opens upward) by finding the zero of the first derivative :
f'(x) = 2x + 2 = 0
2x = -2
x = -1
y = (-1)² + 2×-1 = 1 - 2 = -1
