Step-by-step explanation:
y = x² - 4x + 7
the general vertex form is
y = m(x-h)² + k
to bring the part "x² -4x" to an expression of (ax + b)² we need to add 4, as "x² - 4x + 4" = (x - 2)².
and since we add 4 there, we need to subtract 4 overall again to keep the value of the expression the same :
y = x² - 4x + 4 + 7 - 4 = (x - 2)² + 7 - 4 = (x - 2)² + 3
and so, that is the vertex form :
y = (x - 2)² + 3
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), and a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
Answer:
Please see attachment
Step-by-step explanation:
Please see attachment
Answer:
- The slope is 1/2
- The equation that represents this function is x -2y = 2
Step-by-step explanation:
<em>Intercepts</em>
The table shows the x-intercept to be (2, 0), and the y-intercept to be (0, -1). These are not matched by any of the answer choices.
<em>Slope</em>
The slope is ...
slope = (change in y)/(change in x) = (0 -(-1))/(2 -0) = 1/2
<em>Equation</em>
You can choose the equation by seeing if it works for a couple of points. You know the last equation is incorrect, because that slope-intercept form has the y-intercept as +1, not -1.
