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Thread: Parabola

  1. #1
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    Parabola

    find the value of the discriminant: Use that number to describe the nature of the roots:

    a. 12x^2+2x+5=0

    b. x^2+6x=0


    2: suppose f(x)=3x^2+2x1
    a. find x if f(x)=7
    b. find the x-intercepts
    c. find f(-4)
    d.find (2)
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  2. #2
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    for $\displaystyle ax^2+bx+c=0 $ the discriminant is $\displaystyle \Delta = b^2-4ac$

    When

    $\displaystyle \Delta >0$ your quadratic has two distinct real roots

    $\displaystyle \Delta =0$ your quadratic has one repeated real root

    $\displaystyle \Delta <0$ your quadratic has no real roots

    for $\displaystyle 12x^2+2x+5=0$ then $\displaystyle a = 12, b=2$ and $\displaystyle c = 5$

    so $\displaystyle \Delta = 2^2-4\times 12 \times 5 = \dots$

    finish this and make your conclusion.
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  3. #3
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    Quote Originally Posted by Kayla View Post
    find the value of the discriminant: Use that number to describe the nature of the roots:

    a. 12x^2+2x+5=0

    b. x^2+6x=0
    Do you know that the discriminant of $\displaystyle ax^2+ bx+ c= 0$ is $\displaystyle b^2- 4ac$.


    2: suppose f(x)=3x^2+2x1
    was this supposed to be "+ 1"? I will assume f(x)= 3x^2+ 2x+ 1.

    a. find x if f(x)=7
    Solve 3x^2+ 2x+ 1= 7

    b. find the x-intercepts
    Those are where f(x)= 0. Solve 3x^2+ 2x+ 1= 0.

    c. find f(-4)
    That is just 3(-4)^2+ 2(-4)+ 1.

    d.find (2)
    Assuming you mean f(2), it is just 3(2)^2+ 2(2)+ 1.
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