write the equation of the given parent graph with the points, (5,-2), (6,0), (4,0)
Since we are given three points, we can use the point-slope form of a linear equation to find the equation of the parent graph. The point-slope form is given as:
y - y1 = m(x - x1)
Let's find the slope (m) first:
m = (y2 - y1) / (x2 - x1)
Using (5, -2) and (6, 0):
m = (0 - (-2)) / (6 - 5)
m = (0 + 2) / (1)
m = 2
Now, let's use one of the points and the slope to write the equation:
Using (5, -2):
y - (-2) = 2(x - 5)
y + 2 = 2x - 10
Rearranging the equation in the standard form, we get:
2x - y = 12
So, the equation of the given parent graph is 2x - y = 12.
To determine the equation of the parent graph, we need to identify the type of function and the transformations it undergoes. Without additional information or a graph, it is challenging to determine the exact parent graph or its equation. However, I can provide general examples of some common parent functions and their equations.
1. Linear Function:
The equation of a linear function can be represented as y = mx + b, where m is the slope and b is the y-intercept. For the given points, (5,-2), (6,0), (4,0), we can find the equation of a linear function passing through these points using the slope-intercept form:
Step 1: Find the slope (m):
m = (y2 - y1) / (x2 - x1)
= (0 - (-2)) / (6 - 5)
= 2 / 1
= 2
Step 2: Find the y-intercept (b) by substituting the slope and one of the points (5,-2 into the equation:
-2 = 2(5) + b
-2 = 10 + b
b = -12
The equation of the linear parent graph passing through the given points is:
y = 2x - 12.
2. Quadratic Function:
The equation of a quadratic function can be represented as y = ax^2 + bx + c, where a, b, and c are constants. For the given points (5,-2), (6,0), (4,0), we can find the equation of a quadratic function passing through these points.
Since we have three unknowns (a, b, c) and three points, we can form a system of equations and solve them simultaneously.
Step 1: Substitute the coordinates of the points into the equation y = ax^2 + bx + c:
-2 = a(5)^2 + b(5) + c -- (Equation 1)
0 = a(6)^2 + b(6) + c -- (Equation 2)
0 = a(4)^2 + b(4) + c -- (Equation 3)
Step 2: Solve the system of equations to find the values of a, b, and c. The exact values will be determined through simultaneous substitution or elimination methods.
Once the values of a, b, and c are determined, the equation of the quadratic parent graph passing through the given points will be: y = ax^2 + bx + c.
Without knowing the specific parent graph or having a graph, it is difficult to provide an exact equation. Please provide more information or a clear description of the parent graph, and I will be happy to assist you further.
To write the equation of a parent graph given three points, we need to determine the equation of the graph that passes through those points. However, without knowing the specific shape of the parent graph, we cannot derive an accurate equation.
Can you please provide more details or describe the parent graph?