Does the quadratic have a maximum or minimum
1 answer:
Answer:
B)max/ opens down
Step-by-step explanation:
Parabola equation:
The equation of a parabola has the following format:
If , that is, x² is multiplied by a positive number, the function has a minimum value and the parabola opens up.
If , that is, x² is multiplied by a negative number, the function has a maximum value and the parabola opens down.
In this question:
From the graph, we already see that it opens down and has a max, and analitically, since , this is confirmed. The correct answer is given by option b.
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1. a. Pretty much, you just have to rearrange it so that the highest power is in the front. So, here's your answer:
b. It's a 4th-degree polynomial. A degree means that "what's the highest power?"
c. It's a trinomial. It has 3 terms, hence it's a trinomial.
2. a. Since it's an odd power and a negative coefficient, it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→∞
b. The degree is even and the coefficient is negative, so it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→-∞
3. a. This basically means that if you solve for x, you should get -2, 1, and 2. So, to do this, you can just write it in factored form and multiply inwards using any method of your choice (remember that in the parentheses, you should get the above value if you solve for x):
If you multiply it out, you get (also your answer):
4. The zeros are at x = 3, 2 and -7. Multiplicity of 3 is 1, for 2 it's 2, and for -7 it's 3.
Hope this helps!
b. It's a 4th-degree polynomial. A degree means that "what's the highest power?"
c. It's a trinomial. It has 3 terms, hence it's a trinomial.
2. a. Since it's an odd power and a negative coefficient, it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→∞
b. The degree is even and the coefficient is negative, so it will be:
x→∞, f(x)→-∞
x→-∞, f(x)→-∞
3. a. This basically means that if you solve for x, you should get -2, 1, and 2. So, to do this, you can just write it in factored form and multiply inwards using any method of your choice (remember that in the parentheses, you should get the above value if you solve for x):
If you multiply it out, you get (also your answer):
4. The zeros are at x = 3, 2 and -7. Multiplicity of 3 is 1, for 2 it's 2, and for -7 it's 3.
Hope this helps!