What information can the coefficients a, b, and c give you?
B
Practice makes perfect
We are given a quadratic function written in standard form and we want to find the x -coordinate of the vertex of its graph.
f(x)= ax^2+ bx+ c
Recall that the graph of a quadratic function is a parabola. Then, 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)=2x^2+4x-6 ⇕ f(x)= 2x^2+ 4x+( - 6)
We see that for the given equation a= 2, b= 4, and c= - 6. Consider the point at which the curve of the parabola changes direction.
This point is the vertex of the parabola, and defines the axis of symmetry. Since 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.
The x-coordinate of the vertex is - 1. This corresponds to option B.
Extra
A Common Mistake
One common mistake when identifying the key features of a parabola algebraically is forgetting to include the negatives in the values of these constants. The standard form is addition only, so any subtraction must be treated as negative values of a, b, or c. Let's look at an example.
y=3x^2-4x-2 ⇕ y=3x^2 + (-4x) + (-2)
In this case, the values of a, b, and c are 3, -4, and -2. They are NOT 3, 4, and 2.
a=3, b=4, c=2 *
a=3, b=-4, c=-2 ✓
