Let's start with the intercepts of the given function. The constant of a function tells us the y-coordinate of its y-intercept.
y=x^2-2x -48 ← constant
The y-intercept is (0,-48). To find the x-intercepts, we set y equal to 0 and solve for x.
The graph intersects the x-axis at (8, 0) and at (- 6, 0). Let's include these points in the coordinate plane and draw the parabola.
All parabolas are symmetric about their vertex. What this means is if two points have the same y-coordinate, such as the x-intercepts, they are equidistant from the parabola's line of symmetry. Therefore, we can find the line of symmetry by averaging the x-intercepts.
To find the vertex's y-coordinate, we substitute its x-coordinate into the function and evaluate the right-hand side.
The vertex is at (1,-49). Finally, we want to write the equation in graphing form.
Graphing Form:& y=a(x- h)^2+ k
Vertex:& ( h, k)
Let's substitute the function's vertex in this equation. Notice that the value of a equals the coefficient of x^2. From the equation we see that this is a= 1. With this information, we can write the complete equation.
Function:& y= 1(x- 1)^2+( -49)
Vertex:& ( 1, -49)
This simplifies to y=(x-1)^2-49.
