Lauren describes a parabola where the focus has a positive, nonzero x coordinate. Which parabola(s) could Lauren be describing?
2 answers:
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Answer:
The solution to the system is the pair (9, 6)
Step-by-step explanation:
Hi!
First, let´s write the system of equations:
-y² + 6y + x -9 = 0
6y = x +27
The solutions of the system are the pairs (x, y) that satisfy both equations.
Let´s take the second equation and solve it for x:
6y = x +27
Subtract 27 from both sides of the equation
6y - 27 = x
Now, we can replace x in the first equation and solve it for y:
-y² + 6y + x -9 = 0
-y² + 6y + 6y - 27 -9 = 0
-y² + 12y - 36 = 0
Notice that -y² + 12y - 36 = -(y - 6)², then:
-(y - 6)² = 0
y - 6 = 0
y = 6
(alternatively you can solve the quadratic equation using the quadratic formula).
Now let´s find the value of x:
x = 6y -27
x = 6·6 -27
x = 9
The solution to the system is the pair (9, 6)
Please see the attached figure. The point where the curves intersect is the solution to the system.
Answer:
(2, -2) and (1,-3)
Step-by-step explanation:
The y-intercept means that the coordinate where the line touches the y-axis. In other words, the y value(-4) when x=0. The result is (0, -4). The y coordinate also can be used to fill c variable of y=mx + c
We have 2 coordinates now, (3, -1) and (0, -4), then we can find out the line equation. We need to find the slope (m), the formula will be:
m= y2-y1 / x2-x1=
m= -4 - (-1) / (0-3)
m= -3/-3= 1
The line equation is:
y= mx + c
y= 1x + (-4)
y= x-4
After you have the equation, you can try to test the point individually to find if any of them fit the equation. You can also draw a line on the graph and see if any point touches the graph.
Red dot is the two point we have, red line is straight line that made from both point, and blue point is the option. As you can see on the graph, the points that touch the line will be (2, -2) and (1,-3)
