Given that g(x) = 2x ^ 2 - 2x + 8 , find each of the following. a) g(0) b) g(- 2) C) g(3) d) g(- x) e) g(1 - t)
2 answers:
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Answer:
y-intercept: 10
concavity: function opens up
min/max: min
Step-by-step explanation:
1.) The definition of a y-intercept is what the resulting value of a function is when x is equal to 0.
Therefore, if the function's equation is given, to find y-intercept simply plug in 0 for the x-values:
y intercept ( f(0) )= 10
2.) In order to find concavity (whether a function opens up or down) of a quadratic function, you can simply find the sign associated with the x^2 value. Since 2x^2 is positive, the concavity is positive. This is basically possible, since it is identifying any reflections affecting the y-values / horizontal reflections.
3.) In order to find whether a quadratic function has a maximum or minimum, you can use the concavity of the function. The idea is that if the function opens downwards, the vertex would be at the very top, resulting in a maximum. If a function was open upwards, the vertex would be at the very bottom, meaning there is a minimum. Like the concavity, if the value associated with x^2 is positive, there is a minimum. If it is negative, there is a maximum. Since 2x^2 is positive, the function has a minimum.
The graph of the function f(x) = –x^2 – 4x +2 are true options 1 and 4 are correct.
We have the given,
The graph of the function f(x) = –x^2 – 4x+ 2
The statements that agree with the graph of the equation are as follows:
1. The domain is {x|x ≤ –2}.
<h3>What is the domain?</h3>The set of points at which function is defined.
4. The function is decreasing over the interval (−4, ∞).
From the given graph,
We can say that the above statements are true.
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