3. Modeling With Quadratic Functions
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Try to write the standard form of a quadratic function using the information provided. If it cannot be done, it means that there is no quadratic model for the given set of values.
Yes; y=4x^2
We want to determine whether there is a quadratic function that fits the given set of values.
Given information | Point |
---|---|
f( - 2)= 16 | ( - 2, 16) |
f( 0)= 0 | ( 0, 0) |
f( 1)= 4 | ( 1, 4) |
y=ax^2+bx+c | ||
---|---|---|
Point | Substitute | Simplify |
( - 2, 16) | 16=a( - 2)^2+b( - 2)+c | 4a-2b+c=16 |
( 0, 0) | 0=a( 0)^2+b( 0)+c | c= 0 |
( 1, 4) | 4=a( 1)^2+b( 1)+c | a+b+c=4 |