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Math Help - quadratic function/inequality, multi-step problem and I am stuck

  1. #1
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    quadratic function/inequality, multi-step problem and I am stuck

    Hi everyone, happy Tuesday!

    I am taking algebra and I just don't get quadratics. I have a sheet of different quadratic questions I have been working on since yesterday, trying to figure it out before coming here, but I failed

    I have a couple questions below, thank you in advance for your help

    2. f(x)=2+5x-3x^2
    a. determine if it goes up or down..... down I got that far
    b. find the vertex, this is where I got stuck
    c. find axis of symmetry
    d. find x- and y- intercepts
    e. sketch the graph y=f(x)
    f. determine whether the function has a maximum value or a minimum value, then find this value (What, I am so lost!)
    g. find the range of f.

    ahh why are there so many questions for one function!

    3.) I am stuck on this one because the fractions killed me, er
    solve the quadratic inequality:

    1/2x^2 - 3/4x + 7 <(or equal, didn't know how to add the bar under) 0
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  2. #2
    MHF Contributor
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    Quote Originally Posted by GatorGirl View Post
    2. f(x)=2+5x-3x^2
    a. determine if it goes up or down..... down I got that far
    I don't know what this means...? Since the quadratic is negative, the parabola does open downward....

    Quote Originally Posted by GatorGirl View Post
    b. find the vertex, this is where I got stuck
    To find the vertex, either complete the square or else use the formula "h = -b/(2a)".

    Quote Originally Posted by GatorGirl View Post
    c. find axis of symmetry
    The axis of symmetry is the vertical line "x = h" through the vertex.

    Quote Originally Posted by GatorGirl View Post
    d. find x- and y- intercepts
    To find a given intercept, plug "0" in for the other variable, and solve. So plug "0" in for "x" and evaluate to find the y-intercept, and then plug "0" in for "y" and solve the quadratic equation to find the x-intercept(s).

    Quote Originally Posted by GatorGirl View Post
    e. sketch the graph y=f(x)
    Graph in the usual way: Pick x-values, plug them into the formula, find the corresponding y-values, and draw the dots. Repeat until you are confident of the shape of the curve, and then sketch.

    Quote Originally Posted by GatorGirl View Post
    f. determine whether the function has a maximum value or a minimum value, then find this value (What, I am so lost!)
    Look at the graph. Look at the vertex. Use what you've learned about the relationship between the vertex of a parabola and the max/min points of quadratics.

    Quote Originally Posted by GatorGirl View Post
    g. find the range of f.
    The range is the output values. So look at the graph and figure out what values y can achieve. For instance, can y equal 5?

    Quote Originally Posted by GatorGirl View Post
    3.) solve the quadratic inequality:

    1/2x^2 - 3/4x + 7 <(or equal, didn't know how to add the bar under) 0
    To learn how to answer this, study a lesson on solving quadratic inequalities.
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  3. #3
    Member rtblue's Avatar
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    well. This looks like a perfect opportunity to try out latix , excuse me if i make a mistake.

    I will help you with number 2, how to find the axis of symmetry.

    So.. The Equation is ( i think, someone correct me if i am wrong):

    -3x^2\oplus5x\oplus2

    The formula to find the axis of symmetry is \frac{-b}{2a}

    The standard form of a quadratic equation is: ax^2+bx+c (by the way guys, when i tried to do this in LATEX, it said error...)

    So, just look at your equation, and find the -b(b is 5, so -b is -5) then find the a (the a is -3, -3 times 2 is -6) and plug them into the equation, and that will give you the axis of symmetry.

    So, the axis of symmetry is: \frac{-5}{-6} which simplifies to \frac{5}{6}
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