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What are x and y intercepts of the graph of f(x) = x^2 - 3x + 2 .

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potziunea | Student, Grade 10 | (Level 2) Honors

Posted October 19, 2010 at 8:34 PM via web

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What are x and y intercepts of the graph of f(x) = x^2 - 3x + 2 .

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted October 19, 2010 at 8:35 PM (Answer #1)

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If the parable is intercepting x axis, then the y coordinate for P1 is y=0.

So, the x intercept is obtained when y = 0.

Let's find the x intercept.

x^2 - 3x + 2 = 0

We'll apply the quadratic formula:

x1 = [3+sqrt(9-8)]/2

x1 = (3+1)/2

x1 = 2

x2 = (3-1)/2

x2 = 1

The  x axis intercepts are: (1,0) (2,0).

If the parable is intercepting y axis, then the x coordinate is x = 0.

So, the y intercept is obtained when x = 0.

If x = 0, then y = 0^2 - 3*0 + 2

y = 2

The y axis intercept is (0,2). 

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william1941 | College Teacher | (Level 3) Valedictorian

Posted October 19, 2010 at 8:37 PM (Answer #2)

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At the x intercept the value of y is 0.

f(x) = y= x^2 - 3x + 2 =0

=> x^2 - 2x - x +2 =0

=> x(x-2) -1(x-2) =0

=> (x-1) (x-2) =0

We have x=1 and x=2

Therefore the x intercepts are x=1 and x=2.

For the y- intercept the value of x is 0

=>y= x^2 - 3x + 2 =0 = 0 - 0 +2

So the y- intercept is y=2

Therefore we have the required x-intercepts as the points (1,0) and (2,0) and the required y intercept is (0,2).

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neela | High School Teacher | (Level 3) Valedictorian

Posted October 19, 2010 at 9:58 PM (Answer #3)

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f(x) = x^2-3x+2.

Let f(x) = y.

So y = x^2-3x+2

The y intercept of the curve is got by putting x= 0 in y =x^2-3x+2

So  y = 0^2-3*0+2.

y= 2 is the y intercept, where the curve intersects y axis.

The x intercepts are got by putting y = 0 in the equation y = x^2-3x+2 and solving for x .

f(x) = y =0  gives x^2-3x+2 = 0.

x^2-3x+2 = x^2-2x-x+2

x^2-3x+2 = x(x-2) -1(x-2)

x^2-3x+2 = (x-2)(x-1)

Therefore x^2-3x+2 = 0 implies (x-2)(x-1) = 0.

Therefore (x-2) = 0 or (x-1) = 0

Therefore x = 2 or x = 1 are the  intercepts of the curve on x axis.

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aliddi | High School Teacher | (Level 1) Adjunct Educator

Posted October 20, 2010 at 10:01 AM (Answer #4)

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The y-intercept of the graph is the point where the function crosses the y-axis.  The x-value is equal to zero for every point on the y-axis.

1. Substitute x = 0 into the given function: y = (0)^2 - 3(0) + 2 = 0 - 0 + 2 = 2.  Therefore the y-intercept is at the point (0, 2).

The x-intercept of the graph is the point where the function crosses teh x-axis.  The y-value is equal to zero for every point on the x-axis.

2. Substitute y = 0 into the given function: 0 = x^2 - 3x + 2. 

Since this is a quadratic function we can factor the equation or use the quadratic formula.

3. 0 = x^2 - 3x + 2          (Need to find the factors of 2 whose sum is equal to -3).  (-2) x (-1) = 2 and (-2) + (-1) = -3, so:

0 = (x - 2) (x - 1)

0 = x - 2     and     0 = x - 1          Solve both equations for x.

+ 2    + 2             + 1      +1

2 = x     and     1 = x

The x-intercepts are at 1 and 2, so the coordinates are (1, 0) and (2, 0).

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