Given a quadratic function
y = 4x² - 19x - 5
or i will write it as
4x² - 19x - 5 = y
Zero of the function is when y have the value of zero.
So the quadratic equation will be
4x² - 19x - 5 = y
4x² - 19x - 5 = 0
Now make the equation to intercept form by factorization
4x² - 19x - 5 = 0
(4x + 1)(x - 5) = 0 (this is intercept form)
Solution 1
4x + 1 = 0
4x = -1
x = -1/4
Solution 2
x - 5 = 0
x = 5
SUMMARY
-1/4 and 5 are zero function of f(x) = 4x² - 19x - 5
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Answer:
D. (-3, -2)
Step-by-step explanation:
The equations have different coefficients for x and y, so will have one solution. The solutions offered are easily tested in either equation.
Using (x, y) = (-2, -3):
x = y -1 ⇒ -2 = -3 -1 . . . . False
Using (x, y) = (-3, -2):
x = y -1 ⇒ -3 = -2 -1 . . . .True
2x = 3y ⇒ 2(-3) = 3(-2) . . . . True
The solution is (-3, -2).
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If you'd like to solve the set of equations, substitution for x works nicely.
2(y -1) = 3y
2y -2 = 3y . . eliminate parentheses
-2 = y . . . . . . subtract 2y
x = -2 -1 = -3
The solution is (x, y) = (-3, -2).
The answer to your question is arithmetic
Answer:
<h2>C. G(x) = (x - 1)² - 3</h2>
Step-by-step explanation:
f(x) + n - shift the graph of f(x) n units up
f(x) - n - shift the graph of f(x) n units down
f(x - n) - shift the graph of f(x) n units to the right
f(x + n) - shift the graph of f(x) n units to the left
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Look at the picture.
The graph of F(x) shifted 1 unit to the right and 3 units down.
Therefore the equation of the function G(x) is
In a 30°-60°-90° triangle, the ratio of the legs is
So if the shorter leg is
, then the longer leg is
