What is the image point of (9,4) after a translation left 5 units and up 1 unit?
1 answer:
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Answer:
(- 5, 0 ), (7, 0 )
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (1, - 108 ), thus
y = a(x - 1)² - 108
To find a substitute (0, - 105 ) into the equation
- 105 = a(- 1)² - 108 ( add 108 to both sides )
3 = a
y = 3(x - 1)² - 108 ← equation in vertex form
To find the x- intercepts, let y = 0, that is
3(x - 1)² - 108 = 0 ( add 108 to both sides )
3(x - 1)² = 108 ( divide both sides by 3 )
(x - 1)² = 36 ( take the square root of both sides )
x - 1 = ± = ± 6 ( add 1 to both sides )
x = 1 ± 6, so
x = 1 - 6 = - 5
x = 1 + 6 = 7
x- intercepts are (- 5, 0), (7, 0)
The solution to the system of equations is (-3.88, 0.66) and (3.04, 1.09)
<h3>How to determine the solution to the system of equations?</h3>The system of equations is given as:
x^2y + yx^2 = 20
1/x + 1/y = 5/4
Multiply through the equation 1/x + 1/y = 5/4 by 4xy
So, we have:
4x + 4y = 5xy
So, we have the following system of equations
4x + 4y = 5xy
x^2y + yx^2 = 20
Next, we plot the graph of the system of equations
4x + 4y = 5xy
x^2y + yx^2 = 20
See attachment for the graph of the system
From the attached system, we have the point of intersection to be
(x, y) = (-3.88, 0.66) and (3.04, 1.09)
Hence, the solution to the system of equations is (-3.88, 0.66) and (3.04, 1.09)
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