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
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Answer:
2
Step-by-step explanation:
57x + 1 = 115
57x = 115 - 1
57x = 114
x = 114 / 57
x = 2
Answer:
The equation of the line is:
Step-by-step explanation:
We know that the slope-intercept of line equation is
Where m is the slope and b is the y-intercept
Given the two points on a line
Finding the slope between (0, 3) and (-2, -5)
We know that the y-intercept can be computed by setting x=0 and determining the corresponding y-value.
From the graph, it is clear:
at x = 0, y = 3
Thus, y-intercept = b = 3
Substituting m = 4 and b = 3 in the slope-intercept form of line equation
Therefore, the equation of the line is:
