How can i find the intercept point(s) for the graph Y= X^2 -10X +21?

Question

can you explain it simply so i can understand?

Answer 1

The curve will intercept the x-axis where y = 0. So, solve the equation:

0 = x^2 - 10x + 21

There are a number of ways of solving for x. In this case, it should be easy to see (if you remember your algebra) that the right side of the equation can be factored:

0 = (x - 7)(x - 3)

This means that y = 0 when x = 3 or x = 7. Therefore, the curve intercepts the x-axis when x = 3 and 7.

Answer 2

This is a quadratic equation. The y-intercept is the point where the graph intercepts the y-axis. Therefore, the x-value of the point would be zero. Substitute a zero for the variable "X" in the equation:
Y=0^2-10(0)+21
Y=21
That means the y-intercept is at the point (0,21).

(No calculations were really necessary. For any polynomial equation in the form Y=... the constant term is the y-intercept. The constant term is the term that has no variable in it. It's just a number all by itself.)

Similarly, the x-intercepts are the points where the graph intercepts the x-axis. Therefore, the y-value of the points would be zero. Substitute a zero for the variable "Y" in the equation and then solve it by factoring. This takes a bit more work:

0=X^2-10X+21

We need to find two numbers that multiply to +21 and add up to -10. Look at the product (+21) first. Consider all the ways it can be factored and add up the two factors:

Do this in your head:
(+1) * (+21 )= +21 (+1)+(+21) = +22
(-1) * (-21 )= +21 (-1)+(-21) = -22
(+3) * (+7 ) = +21 (+3)+(+7) = +10
(-3) * (-7 ) = +21 (-3)+(-7) = -10

There they are! -3 and -7 have a product of +21 and a sum of -10. They are the two numbers we are looking for:

We can now write the next line of our solution:

0=(X-3)(X-7)

Now, let's think about what this equation means: Two unknown values are being multiplied together and the result is zero. The only way we could get a product of zero is if one of the two unknown numbers is already zero. Write each of these possibilities as an equation, and then solve the two simple equations:

X-3 = 0 or X-7 = 0
X=3 or X=7

The x-intercepts are found at (3,0) and (7,0).

Answer 3

the quadratic equation is
y = x² - 10x + 21
You are to find the intercept points.

The intercept points are the points of intersection of the graph and the x and y axes. The intersection with the x-axis are the x-intercepts and the intersection with the y-axis are the y-intercepts. What intersections?

If you graph y = x² - 10x + 21, you will notice that it is a "parabola," a certain kind of curve. To see how a parabola looks like, take arbitrary points for x (such as -3,-2,-1, 0, 1, 2, 3) and substitute them to the equation.
Record your results
(x,y)
(2,5)
(3,0)
(4,-3)
(5,-4)
(6,-3)
(7,0)
(8,5)

If you plot these points in the coordinate plane, you will notice that they form a curve. It intercepts the x and y axes. These are the values we want to find.

You will notice that the points of intersections to the x-axis has the y-coordinate equal to zero and the point of intersection to the y-axis has the x-coordinate equal to zero. This is how we solve for the intercepts.

the parabola equation is
y = x² - 10x + 21
If we let x = 0 (solving for the y-intercept/s)
y = (0)² - 10(0) + 21
y = 0 - 0 + 21
y = 21
Therefore,
(0,21) is an intercept point, specifically a y-intercept (since x = 0) If you try to plot this point, you will see that it is a part of the parabola graph of the equation (if you extend the curve), and it is the intersection of the curve and the y-axis(thus, y-intercept).

If we now let y = 0 (solving for the x-intercept),
0 = x² - 10x + 21
x² - 10x + 21 = 0
(x - 7)(x - 3) = 0
x - 7 = 0
x = 7 and
x - 3 = 0
x = 3

Therefore, the points (7,0) and (3,0) are intercept points, specifically x-intercepts (since y = 0)
You will notice that these points are the intersections of the parabola graph and the x-axis(thus x-intercept).



Therefore,
The intercept points are (0,21) (a y-intercept), (7,0) (an x-intercept) and (3,0) (also an x-intercept)

I hope you understood^_^

^_^

Answer 4

Create a table with two rows, x and y with 10 columns.
In each column in the x row, put in the numbers from 0 - 9
Work out the value of y for every value of x and put it in the corresponding column in the y row.

Should look something like this:

x 0 1 2 3 4 5 6 7 8 9
y 21 13 5 0

work out the rest of the y values for x between 4 to 9

plot a graph, with x in the horizontal axis and y in the vertical axis,
with the points you have worked out.

the x-intercept points are the points where the curve crosses the x-axis (ie. where y is/are zero) and the y-intercept point is where the curve crosses the y-axis (where x is zero)

Answer 5

Y-intercepts:

Set "x = 0", and solve for Y

Y= X^2 - 10X + 21 -----> Y= (0)^2 - (0)X + 21 = 21

Y-intercept = (0 , 21)


X-intercepts:
Set "y = 0", and solve for X

Y= X^2 - 10X + 21 -----> 0 = X^2 - 10X + 21
(X - 3)(X - 7) = 0 [Factoring, trial and error...]

X = 3 or 7

X-intercepts are (3 , 0) and (7 , 0)

Answer 6

If u want the x-intercepts, then find where y=0.

Make x^2 -10x + 21 = 0.

(x-7)(x-3) = 0

x= 7
or
x=3.

If you want the y-intercepts, make x=0.

y=0^2 - 10 (0) +21

y= 0+0+21

y=21!!!!

Answer 7

x^2 - 10x + 21 = (x - 7)(x - 3)
x = 7 or 3

Answer 8

to find the Y intercept, set the Y value to zero and solve for x (y will be zero). To find the x intercept, set the x values to zero and solve for y (x will be zero).