|3x-7| + 7 = 9 What is the first solution? Plzzz help
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The x-intercepts of the parabola are (3, 0) and (7,0)
<h3>How to determine the x-intercept?</h3>The given parameters are:
Vertex (h, k) = (5, -12)
Point (x, y) = (0, 63)
The equation of a parabola is:
y = a(x - h)^2 + k
Substitute (h, k) = (5, -12)
y = a(x - 5)^2 - 12
Substitute (x, y) = (0, 63)
63 = a(0 - 5)^2 - 12
Evaluate
63 = 25a - 12
Add 12 to both sides
25a = 75
Divide by 26
a = 3
Substitute a = 3 in y = a(x - 5)^2 - 12
y = 3(x - 5)^2 - 12
Set y to 0 to determine the x-intercepts
0 = 3(x - 5)^2 - 12
Add 12 to both sides
3(x - 5)^2 = 12
Divide by 3
(x - 5)^2 = 4
Take the square root of both sides
Add 5 to both sides
Expand
x = (5 - 2, 5 + 2)
Evaluate
x = (3, 7)
Hence, the x-intercepts of the parabola are (3, 0) and (7,0)
Read more about parabola at:
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Answer:
Step-by-step explanation:
When making a matrix of two equations with the variables x and y, the result will be a matrix with three columns:
- a column for the values of x in each equation
- a column for the values of y in each equation
- a column for the independent values of each equation
since our system of equations is:
we can see that the value for x in the first equation is 3 and in the second equation is 4, thus the first column will have the numbers 3 and 4:
Now for the values of y we hvae -5 in the first equation and -2 in the second equation, we update the matrix with another column with the values of -5 and -2:
Finally, the last column is the independent values of each equation (or the results) in the first equation that number is 12 and in the second equation is 15, thus the matrix is:
usually there is a line separating the columns for the values of x and y, and the independent values:
this is the matrix of the system of equations