Try to write the standard form of a quadratic function using the information provided. If you cannot do it, it means that there is no quadratic model for the given set of values.
Does a Quadratic Model Exist? Yes. Equation: y=5/8x^2-7/4 x+1
Practice makes perfect
We want to determine whether there is a parabola that fits the given set of values.
Given information
Point
f( - 2)= 7
( - 2, 7)
f( 0)= 1
( 0, 1)
f( 2)= 0
( 2, 0)
To use the given points, we need to substitute their ( x, y) coordinate pairs into the standard form of a quadratic function.
y=a x^2+b x+c, a≠0
Doing so will create a system of equations that we can solve for the values of a, b, and c. Let's start with (0,1).
We now have a system of two equations.
4a+2b=- 1 & (I) 4a-2b=6 & (II)
Let's solve this system using the Elimination Method. Since the b-variable has opposite coefficients in both equations, we will start by adding Equation (I) to Equation (II).
Now that we have a= 58, b=- 74, and c=1, we can write the full equation of the quadratic function.
y=5/8x^2+( - 7/4 )x+1 ⇔ y=5/8x^2-7/4 x+1
To help visualize this graph, we have plotted the given points and sketched the curve below.
