How do you graph the parabola #h(t)=-16t^2+280t+17 # using vertex, intercepts and additional points?

Answer 1

Graph parabola

The main features to graph this parabola are: 1. It is downward because a < 0 2. Vertex. x-coordinate of vertex: #x = -b/(2a) = -280/-32 = 35/4# y-coordinate of vertex: #y(35/4) = - 16(1225/16) + 280(35/4) + 17# 3. y-intercept. Make x = o, y-intercept --> 17 4. x-intercepts. Make y = 0 andsSolve the quadratic function by the new improved quadratic formula in graphic form (Socratic Search) #y = -16x^2 + 280x + 17 = 0# #D = d^2 = b^2 - 4ac = 32,400 + 1088 = 33,488# --> #d = +- 183# There are 2 x-intercepts (real roots); #x = -b/(2a) +- d/(2a) = -280/32 +- 183/32 = 35/4 +- 183/32#
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Answer 2

To graph the parabola h(t) = -16t^2 + 280t + 17, you can start by finding the vertex, intercepts, and additional points.

  1. Vertex: The vertex of a parabola in the form h(t) = at^2 + bt + c is given by the point (h, k), where h = -b/(2a) and k = h(h).

  2. Intercepts: To find the y-intercept, set t = 0 and solve for h(0). To find the x-intercepts, set h(t) = 0 and solve for t.

  3. Additional Points: Choose additional values of t to evaluate h(t) and plot those points on the graph.

Once you have these points, you can plot them on a graph and sketch the parabola passing through these points.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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