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If f(x)=a x^2+b x+c is a quadratic funct...

If `f(x)=a x^2+b x+c` is a quadratic function such that `f(1)=8,f(2)=11` and `f(-3)=6` find `f(x)` by using determinants. Also, find `f(0)dot`

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To solve the problem, we need to find the quadratic function \( f(x) = ax^2 + bx + c \) given the conditions \( f(1) = 8 \), \( f(2) = 11 \), and \( f(-3) = 6 \). We will use determinants to find the coefficients \( a \), \( b \), and \( c \). ### Step 1: Set up the equations From the given conditions, we can set up the following equations: 1. \( f(1) = a(1)^2 + b(1) + c = 8 \) This simplifies to: ...
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Knowledge Check

  • If f(x) is a quadratic function such that f(0)=3,f(1)=6 and f(2)=11 , then: f(x)=

    A
    `2x^3+x+3`
    B
    `x^3+x+3`
    C
    `x^3+2x+3`
    D
    none of these.

  • If f is a function such that f(0) = 2, f(1) = 3, f(x+2) = 2f(x) - f(x + 1), then f(5) is

    A
    `-3`
    B
    `-5`
    C
    7
    D
    13

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