<span><span>2x(x - 5) + 3(x - 5) (rewriting expression)
</span><span>2x(x) - 2x(5) + 3(x) - 3(5) (applying distributive property)
</span><span>2x^2 - 10x + 3x - 15 (simplifying)
</span><span>2x^2 - 7x - 15 (combining like terms)
I found this as an example from research. I do hope this helps. I have trouble in the same subject or I used to anyway. I hope this is what you were looking for. :)</span></span>
Answer:
B
Step-by-step explanation:
just think about it :
can it move up or down ? no, because for a specific input value still the same functional result is calculated (nothing is getting bigger or smaller).
all that is happening that way is that now, with using g(x), the original f(x) functional values happen now 2 units "later" = to the right (if you consider the x-axis a time line growing to the right). we are getting the functional value of f(x-2) at x and not at x-2 for g(x).
for example
the functional values are for x² (just some integers to make it easier) :
x = 1, 2, 3, 4, 5, ...
getting
f(1), f(2), f(3), f(4), f(5), ...
leading to
1², 2², 3² 4², 5², ...
which is
1, 4, 9, 16, 25, ...
now, let's say we start looking at x = 3
x = 3, 4, 5, 6, 7, ...
getting
g(3), g(4), g(5), g(6), g(7), ..
leading to
1², 2², 3² 4², 5², ...
which is
1, 4, 9, 16, 25, ...
so, now we are getting the functional value at e.g. x = 5 that we got originally for x = 3 (9).
therefore, under g(x) the original functional values still "happen", they just simply "happen" 2 units "later" (to the right).
in the same way
g(x) = f(x+2) moves everything 2 units to the left (now things are happening "earlier").
The intercepts and the standard form of each polynomial are listed below:
- x-Intercept: x = - 4 or x = 6, Standard form: f(x) = x² - 2 · x - 24, y-Intercept: f(0) = - 24
- x-Intercept: x = 1 / 4 or x = 3, Standard form: f(x) = 2 · x² - 10 · x + 12, y-Intercept: f(0) = 12
<h3>How to find the intercepts and the standard form of quadratic equations</h3>
In this case we need to find the intercepts of each quadratic equation and transform each quadratic equation into standard form. The x-intercept correspond with each of the roots of the polynomial and the y-intercept is found by evaluating the expression at x = 0.
Now we proceed to find each element:
Case 1
x-Intercept
x = - 4 or x = 6
Standard form
f(x) = (x + 4) · (x - 6)
f(x) = x² - 2 · x - 24
y-Intercept
f(0) = - 24
Case 2
x-Intercept
x = 1 / 4 or x = 3
Standard form
f(x) = (2 · x - 4) · (x - 3)
f(x) = 2 · (x - 2) · (x - 3)
f(x) = 2 · (x² - 5 · x + 6)
f(x) = 2 · x² - 10 · x + 12
y-Intercept
f(0) = 12
To learn more on quadratic equations: brainly.com/question/1863222
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Answer:
x = 2y - 5
Step-by-step explanation:
