Function Graph Help: y = –(3/8)x^2 + 8.?

Question

Sketch the graph of the function y = –(3/8)x^2 + 8.
What are the domain and range of the function?
What are the x-intercepts? Approximate to two decimal places.



ANSWERS:

a. domain = (–∞, ∞); range = (–∞, 8];
x-intercepts: points (–4.62, 0) and (4.62, 0)

b. domain = (–∞, ∞); range = (–∞, 8];
x-intercepts: none

c. domain = (–∞, 8]; range = (–∞, ∞);
x-intercepts: points (–4.62, 0) and (4.62, 0)

d. domain = (–∞, 8]; range = (–∞, ∞);
x-intercepts: points (–1.63, 0) and (1.63, 0)

Answer 1

You can conclude the answer with no calculations at all.
Since this is a quadratic function (x^2), then the domain will always be from -∞ to +∞ so the domain is ( -∞, ∞)

The formula y = x^2 has a graph of a parabola, concave up, with vertex at x=0 and y=0. If you add a constant to the formula, then you increase the y-intercept so that it would be that constant.
so the constant in your equation is +8, with which we conclude that the range is either from 8 to ∞, or from -∞ to 8. This depends on the coefficient of x^2. Since x^2 in your equation has a negative coefficient, this means that the parabola is concave down. And since the vertex is at y=8, then this is the largest value of y, and hence y<=8, so the range is between (-∞ ,8)

so domain = (–∞, ∞); range = (–∞, 8), which is the first choice, without even solving for the x-intercept. so the answer is a.
Of coursw you know that there should be 2 x-intercepts, since the graph is concave down, with the largest y value being a positive value. So the graph will cross the x-axis in two points.

Answer 2

I agree with answer a. quadratic formula gives -4.62 and 4.62 for x-intercepts, eliminating b and d. The domain of the function is all reals which leaves you with answer a.

Answer 3

The domain is infinite - only a and b are possible answers.

Of the two, a is correct because it lists a range that crosses the x-axis (i.e., crosses zero) and therefore MUST have x-intercepts. Answer b lists no x-intercepts and must therefore be incorrect.

Choose a.

Answer 4

i think a is true
a. domain = (–∞, ∞); range = (–∞, 8];
x-intercepts: points (–4.62, 0) and (4.62, 0)

Answer 5

for a graph, go to http://www.calculator.com/calcs/GCalc.html

y = (-3/8)x^2 + 8

ANS : a.)

Answer 6

Would say that it is answer a but I'm not sure...