Having written the function in graphing form, we can identify the vertex.
Graphing Form:& y=(x-( - 5/2))^2+ 3/4
Vertex:& ( - 5/2, 3/4)
b
In any function the y-intercept is given by its constant. If we examine the function, we can identify the function's constant as 7.
y=x^2+5x+ 7
We could also determine this by substituting x=0 into the function and simplifying.
c
Examining the function, we see that the x^2-term's coefficient is positive. This means that the parabola must open upwards. Let's plot the vertex and y-intercept from Parts A and B. Let's also include the parabola's line of symmetry, which is a vertical line through the parabola's vertex.
The parabola's symmetry allows us to identify a third point through which the line passes that is on y=7. This point will be equidistant with the y-intercept from the line of symmetry.
The third point is at (- 5,7). Now we can draw an accurate parabola.
