# Parabolas, graphing, quadratic equations

***See attached file for full problem description.***

For questions 18, 20, 22, 24, complete the table by matching each graph with the correct equation from (a) - (h).

For each equation in exercises 25 to 28, identify the axis of symmetry, create a suitable table of values, and sketch the graph (including the axis of symmetry).

For each equation in exercises 29 to 34, find the x-intercepts.

6. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle.

22. The equation h = -16t2 + 112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180 ft.

36. A ball is thrown upward from the roof of a building 100 m tall with an initial velocity of 20 m/s. When will the ball reach a height of 80 m?

46. The demand equation for a certain type of printer is given by D = -200p + 35,000. The supply equation is predicted to be S = -p2 + 400p - 20,000. Find the equilibrium price.

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#### Solution Preview

For questions 18, 20, 22, 24, complete the table by matching each graph with the correct equation from (a) -(h).

18. This is a line with a slope of -1 and a y-intercept of 1. So, it looks like y = -x + 1. That means that the answer is d.

19. This is a parabola that is shifted right and down. The answers that are parabolas are: a, c, e, f, and h. It can't be a or e, because the graphs of those would open downwards. It can't be f because that graph would be shifted up. And, it can't be h, because that graph isn't shifted at all. That means the answer is f.

20. By the same logic as in 19, the only answer that works is h.

21. This is a line with a slope of 1 and a y-intercept of 1, so it's equation is y = x + 1. ...