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Math Help - Linear Functions

  1. #1
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    Linear Functions

    • Given P(x) = x^2+7x+c and P(-3)=3, find c.

    If I were to do this i would sub in -3 for x so...
    3=-3^2+(7x3)+c
    3 = 9+21+c
    3 = 30+c
    c=-27
    But im not sure if this is right?


    Also
    • for the linear function f. It is known that f(1)=1 and f(-2)=-8. Find the function rule.
    I am a little stuck with this one and unsure how to approach it??
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by scubasteve94 View Post
    • Given P(x) = x^2+7x+c and P(-3)=3, find c.

    If I were to do this i would sub in -3 for x so...
    3=-3^2+(7x3)+c
    3 = 9+21+c
    3 = 30+c
    c=-27
    But im not sure if this is right?
    almost. you will have 3 = 9 - 21 + C

    Also
    • for the linear function f. It is known that f(1)=1 and f(-2)=-8. Find the function rule.

    I am a little stuck with this one and unsure how to approach it??
    note that you have the points (1,1) and (-2,-8) on the line. you can use these to find the slope of the line (do you know how?), once you have that, you can find the equation of the line, which is the rule you are looking for. it will be of the form y = mx + b, where m is the slope, and b is the y-intercept
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    almost. you will have 3 = 9 - 21 + C
    so it will be
    3 = 9 -21 + C
    3 = -12 + C
    C = 15

    Quote Originally Posted by Jhevon View Post
    note that you have the points (1,1) and (-2,-8) on the line. you can use these to find the slope of the line (do you know how?), once you have that, you can find the equation of the line, which is the rule you are looking for. it will be of the form y = mx + b, where m is the slope, and b is the y-intercept
    so
    y = mx + b
    y = (1/3)x + b
    sub in point (1,1) to find b
    1 = (1/3)x1+b
    b = (2/3)
    therefore f(x) = (1/3)x + (2/3)
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by scubasteve94 View Post
    so it will be
    3 = 9 -21 + C
    3 = -12 + C
    C = 15
    yes

    so
    y = mx + b
    y = (1/3)x + b
    sub in point (1,1) to find b
    1 = (1/3)x1+b
    b = (2/3)
    therefore f(x) = (1/3)x + (2/3)
    no. recall the slope formula for the slope between points (x_1,y_1) and (x_2,y_2). it is: \frac {y_2 - y_1}{x_2 - x_1}
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  5. #5
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    Quote Originally Posted by Jhevon View Post
    no. recall the slope formula for the slope between points (x_1,y_1) and (x_2,y_2). it is: \frac {y_2 - y_1}{x_2 - x_1}
    so it would be
    y = mx + b
    y = 3x + b
    sub point (1,1) to find b
    1 = 3x1 + b
    1 = 3 + b
    b = -2
    therefore f(x) = 3x - 2
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by scubasteve94 View Post
    so it would be
    y = mx + b
    y = 3x + b
    sub point (1,1) to find b
    1 = 3x1 + b
    1 = 3 + b
    b = -2
    therefore f(x) = 3x - 2
    yes
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  7. #7
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    thank you so much
    you were a lot of help
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