y=-4(x-2)2+2

Question

i have to explain the 5 points and show the work

Answer 1

y =-4(x-2)^2 + 2

is a quadratic equation in vertex form

y =a(x-h)^2 + k where (h,k) is the vertex

immediately you can find one point you can read off: the vertex (2,2) = maximum point of a downward opening parabola

then expand to find the y intercept: -4x^ +8x -16 +2. y intercept is -16+2 = -14 the point (0,-14)

that's 2 points. Another 3rd point is symmetric about the line of symmetry: x=2

(0,-14) is symmetric about x=2 with the point (4,-14). That's a 3rd point

the other two points most readily found are the x intercepts

found by setting the polynomial = 0

0=-4(x-2)^2 +2 solve for x, that will give 2 more points

0=-4x^2 +16x -16 +2

4x^2 -16x + 16 -2 = 0

4x^2 -16x = -14

2x^2 - 8x = -7

2(x-4x + 4) = -7 +8

2(x-2)^2 =1

(x-2)^2 = 1/2

x-2 = sqr(1/2

x = 2 + or -sqr(1/2) = the roots or zeros

these are two points

(2+sqr(1/2), 0) and (2-sqr(1/2), 0)

= about (2.707, 0) and (1,293, 0)

that's "5 points," which is the MARTA station (major railroad connection) in downtown Atlanta, which you should probably avoid after dark. The City Council even once considered labeling the area a "terrorist zone" An Air Force veteran once set himself on fire down there, and he died, from major burns before anyone could help. Also the place where Wendy's burned down after a drunk customer was shot by police. But if you're brave, you can brag to friends you survived a war zone. Be in shape physically though, so you can run. Elderly and disabled advised to avoid the area.

but mathematicians are more "objective" ie amoral and know nothing except abstract logic and abstract numbers, which may or may not exist, depending on how neo-Platonic you are. Plato believed the "forms" were more real than the earthly shadows of reality. Most mathematicians consider numbers as artificial constructs of the mind. Dissenters see them as really existing in another plane or dimension of existence, much like Plato.