What information can the coefficients a, b, and c give you?
( - 2.5, - 36.75)
Practice makes perfect
We have a quadratic function written in standard form.
f(x)=ax^2+bx+c
This kind of equation can give us a lot of information about the parabola by observing the values of a, b, and c.
f(x)=3x^2+15x-18
⇕
f(x)=3x^2+15x+(-18)
We see that for the given equation a=3, b=15, and c=- 18.
The point at which the graph of a parabola changes direction defines the maximum or minimum point of the graph. Whether the parabola has a minimum or maximum is determined by the value of a.
Since the given value of a is positive, the parabola has a minimum value at the vertex. Therefore, to find the lowest point of the graph we need to find the vertex.
If we want to calculate the x-value of this point, we can substitute the given values of a and b into the expression - b2a and simplify.
Given the standard form of a parabola, the ( x, y) coordinates of its vertex can be expressed in terms of a and b.
( x, y) ⇔ ( - b/2a, f(- b/2a ) )
We have already calculated both of these values above, so we know that the vertex lies on the point ( - 2.5, -36.75). Therefore, the lowest point of the graph is (- 2.5, - 36.75).
