The vertex form of the quadratic function f(x) = x² + 2x + 3 is given as follows:
f(x) = (x + 1)² + 2
<h3>What is the equation of a parabola given it’s vertex?</h3>
The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
In this problem, the function is:
f(x) = x² + 2x + 3
Completing the squares, we find the equation in vertex form, as follows:
f(x) = (x + 1)² + 2
As (x + 1)² = x² + 2x + 1, hence 2 has to be added to find the equivalent function.
More can be learned about quadratic functions at brainly.com/question/24737967
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Answer <u>(assuming it can be in slope-intercept form)</u>:
Step-by-step explanation:
1) First, find the slope of the line between the two points by using the slope formula, 
. Substitute the x and y values of the given points into the formula and solve:
Thus, the slope of the line is 
.
2) Next, use the point-slope formula 
to write the equation of the line in point-slope form. Substitute values for 
, 
, and 
in the formula.
Since represents the slope, substitute in its place. Since and represent the x and y values of one point the line intersects, choose any of the given points (it doesn't matter which one, it will equal the same thing) and substitute its x and y values into the formula as well. (I chose (-2,0), as seen below.) Then, isolate y and expand the right side in the resulting equation to find the equation of the line in slope-intercept form:
Answer:
Interestingly, the likelihood of a randomly chosen student being a female is <u><em>0.58</em></u> at this school.
Step-by-step explanation:
This school features more female students than male students. <em>Consequently, if resources are allocated equally (because it has been found that both female and male male students are similarly likely to be involved), the number of female students involved in after-school athletics programs is greater than the number of male students and could clarify the facilities issues.</em>
Answer:
b. x = 80, y = 100, z = 63
Step-by-step explanation:
Answer:
0 to 4.5
Step-by-step explanation:
ranges from 0 to 4.5
