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brodybb9350
22.12.2020 •
Mathematics
Given 2x (x + 1) - 3 (x + 1), what can be done to simplify for factoring?
A.
Subtract 2x.
B.
Factor out (x+ 1).
C.
Add 3.
D.
Multiply by (x + 1).
Solved
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Ответ:
C) The y-intercept will always be the vertex.
Step-by-step explanation:
We have the quadratic function in the form:
And we want to determine the true statement when b = 0.
Let's go through each of the choices and examine its validity.
Choice A)
Recall that according to the quadratic formula, the roots of a function is given by:
If b = 0, then we acquire:
As we can see, as long as the inside of the square root is positive, the graph will have x-intercepts. So, b equalling zero does not guarantee that the graph does not have any x-intercepts.
A is false.
Choice B)
A quadratic has a minimum if it curves upwards and a maximum if it curves downwards.
This is decided by the leading coefficient a. b does not affect whether a quadratic curves downwards or upwards.
B is false.
Choice C)
The vertex of a quadratic is given by:
If b = 0, then the x-coordinate of the vertex is given by:
Then the y-coordinate will be:
So, the vertex is (0, c).
This is also the y-intercept as, by definition, the y-intercept is the value when x = 0.
So, Choice C is the correct choice.
Choice D)
The axis of symmetry is the x-coordinate of the vertex. As we saw earlier, the x-coordinate of the vertex will always be:
Zero is neither positive nor negative. Thus, D is false.