What is the orientation of the parabola if a>0? What about if a<0? How do you find the equation of the axis of symmetry and the x-coordinate of the vertex? What value gives the y-intercept of the function?
See solution.
Practice makes perfect
Consider the standard form of the equation of a quadratic function.
y=ax^2+bx+c, with a≠0
We want to determine how the values of a, b, and c affect the graph. Let's consider them one at a time.
Value of a
If a>0, the parabola opens upward. Therefore, the vertex is a minimum. Conversely, if a<0, the parabola opens downward. In this case, the vertex is a maximum. Consequently, the value of a defines the orientation of the parabola, and whether the vertex is a minimum or a maximum.
Note also that a is the leading coefficient. Therefore, the greater the value of |a|, the narrower the parabola is.
Value of b
Now, let's recall the formula for the axis of symmetry.
x=- b/2a
We can see that, apart from the value of a, the axis of symmetry depends on the value of b. Furthermore, since the axis of symmetry is the vertical line through the vertex, the x-coordinate of the vertex is also given by the above formula. Therefore, both the axis of symmetry and the position of the vertex will depend on the value of b.
Value of c
The value of c is the y-intercept of the parabola.
