Question

What are the x- and y-intercepts of the graph of y = x2 − 10x + 21? x-intercepts: (−3, 0) and (−7, 0) y-intercept: (0, −21) x-intercepts: (7, 0) and (3, 0) y-intercept: (0, 21) x-intercepts: (3, 0) and (7, 0) y-intercept: (0, −21) x-intercepts: (−3, 0) and (−7, 0) y-intercept: (0, 21)

Answer 1

(3,0) and (7,0) are the x-intercepts ,(0,21) is the y-intercept.

Explanation:

We have given the equation:

y = x² − 10x + 21

We have to find the x-intercept and y-intercept of the equation.

For y-intercept put x = 0 we get,

y = (0)²-10(0)+21

y = 21 is the y-intercept.

For x-intercept put y = 0 we get:

x²-10x+21 = 0

x²-7x-3x+21 = 0

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

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

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

x = 7 or x = 3

x = 7 , x = 3 are the x-intercepts of the equation.

Answer 2

x-intercepts: (7, 0) and (3, 0) y-intercept: (0, 21)

Explanation:

To find the intercept of the graph with the y-axis, do x = 0 and clear the variable y as shown below:

`y = x ^ 2 - 10x + 21\\\\y = (0) ^ 2 - 10(0) + 21\\\\y = 21`.

To find the intercept with the x-axis, do y = 0 and clear x.

`y = x ^ 2 - 10x + 21\\\\x ^ 2 - 10x + 21 = 0`

To solve this equation we must factor the expression.

To write the polynomial of the form:

`(x-a)(a-b) = 0`

we must find two numbers that when adding them obtain as result -10 and when multiplying both numbers obtain as result +21.

These numbers are: -3 and -7.

`-3 -7 = -10\\\\(-3)(-7) = +21`

So, we have:

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

Clearly the solutions to the equation are:

`x = 3`

`x = 7`

These are the intercepts of the parabola with the x-axis