Let's start with the intercepts. The constant of a function tells us the y-coordinate of its y-intercept.
y=x^2+2x - 80 ← constant
The y-intercept is (0,- 80). 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 (- 10, 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 y-coordinate, we substitute its x-coordinate into the function and evaluate the right-hand side.
The vertex is at (-1,-81). 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+( -81)
Vertex:& ( -1, -81)
This simplifies to y=(x+1)^2-81.
