the graph is moved down 6 units
It can be anything from 41/4 to infinite.
x1:y1 = x2:y2 4:-2 = x2:5 x2 = (4*5)/-2 x2 = -10
You can get it to vertex form by completing the square: y = x2 + 7x + 4 ∴ y = x2 + 7x + (7/2)2 - (7/2)2 + 4 ∴ y = (x + 7/2)2 - 49/4 + 16/4 ∴ y = (x + 7/2)2 - 33/4
The vertex has a minimum value of (-4, -11)
y = x2 + 4 The graph is a parabola, with its nose at y=4 on the y-axis, and opening upward.
the graph is moved down 6 units
It can be anything from 41/4 to infinite.
y = x2 - 4x + 4 can be factored into y = (x-2)(x-2) The repeated factor is 2.
y = x2-4x+4 Since the highest degree term is 2, it must have 2 roots
x1:y1 = x2:y2 4:-2 = x2:5 x2 = (4*5)/-2 x2 = -10
You can get it to vertex form by completing the square: y = x2 + 7x + 4 ∴ y = x2 + 7x + (7/2)2 - (7/2)2 + 4 ∴ y = (x + 7/2)2 - 49/4 + 16/4 ∴ y = (x + 7/2)2 - 33/4
The vertex has a minimum value of (-4, -11)
x2 + 2y = 52 + 2*2 = 25 + 4 = 29
y ≥ 11
y = 4x-3
It is linear in y, quadratic in x. Generally, that would be considered a quadratic.