The axis of symmetry is x=-b/2a for f(x), the axis of symmetry is x=0, because there is no b. when x=0, f(x)=4*0²-1=-1, so the vertex is (0, -1) because a in this case is 4, a positive number, the parabola opens upward, -1 is the lowest value.
for g(x), x=-(-8)/2*1=4, f(x)=4²-8*4+5=-11, the vertex is (4,-11) because a is 1 in this case, a positive number, the parabola opens upward, -11 is the lowest value.
for h(x), x=-(-12)/[2*(-3)]=-2, f(x)=-3*(-2)²-12(-2)+1=13, the vertex is (-2,13) because a is -3 in this case, a negative number, 13 is the largest value.
f(x)'s is obviously larger than g(x) (the graph of f(x) is above that of g(x)), but for h(x), since it opens downward from y=13, it overwraps with part of f(x) and g(x), I'm not sure how you can compare that.
but if we look at the vertex alone, g(x) is the least, then f(x), then h(x) is the largest. I hope all this makes sense.
The answer is actually A g(x) is the lowest amount, h(x) being the middle, and f(x) being the largest, I see where you were going with it, but I think you miscalculated f(x), because it is larger than h(x)
The length of the rectangle is based on its width, so let's call width w and put the length in terms of the width. We are told that the width is 45 less than 4 times the width, so the length is 4w - 45. Area is found by multiplying length times width and we are given the area as 3325. So we will set up length times width and solve for w, which we will then use to solve for l. 3325 = (4w - 45)(w). Multiplying out we have . Move the constant over by subtraction and then we will have a quadratic that can be factored to solve for w. . We would put that through the quadratic formula to solve for w. When we do that we get that w = 35 and w = -23.75. The 2 things in math that will never EVER be negative is time and distance/length, so -23.75 is out. That means that the width is 35. The length is 4(35) - 45 which is 95. The dimensions of your rectangle are length is 95 and width is 35. There you go!
Break up the figure into easier figures, a small square and a bigger square.
Small square- 3*2*1 = 6 cm
Large Square- 7*6*1 = 42 cm
42 + 6 = 48 cm. But wait! You have to take one more step, which is minus-ing 6 from 48. Why? Notice that there is a little area where a side of the small square meets the bigger square. That little area is worth 3 cm ( length is 3, height is 1 cm ) times 2 ( 3 cm is one side, another 3 cm is the other side from the other square ) = 6 cm.
Your total answer should be 42. ( or 48, if your teacher doesn't count the area where the squares meet/join together ).
