What are x and y intercepts of the graph of f(x) = x^2 - 3x + 2 .
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write10 answers
starTop subject is Math
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).
Related Questions
- What are the x-intercepts of y = 2x^2 - 3x – 20
- 1 Educator Answer
- Find the x intercepts of the graph of y = -x^2 + 3x + 18
- 2 Educator Answers
- `f(x) = x^3 + 2, 3x - y - 4 = 0` Find an equation of the line that is tangent to the graph...
- 2 Educator Answers
- What are the intercepts of y= x^2 -4x + 5 ?
- 2 Educator Answers
- Find the domain, range, asymptote, the x and y intercepts then graph: y= f(x)= 3^(x-2)
- 1 Educator Answer
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.
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).
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).
Student Answers