Question

The function g(x) = x2 - 10x + 24 is graphed on a coordinate plane. Where will the function cross the x-axis?

© (-6, 0) and (-4,0)
(-2, 0) and (-12, 0)
(4,0) and (6,0)
(12, 0) and (2,0)
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Answer 1

(4, 0) and (6, 0)

Explanation:

The function that we have is:

`g(x)=x^2-10x+24`

This is the function of a parabola.

to find the points where the function crosses the x-axis, we need to find the values of x for which g(x) (which is the value of the y-axis) is equal to zero.

so we need
`g(x)=0` for the function to be crossing the x-axis.

Thus our equation becomes:

`x^2-10x+24=0`

and we can solve this equation with the quadratic formula or by factoring.

I will sove by factoring:

To factor this type of equations we need to find 2 number that satisfy the following:

• when multiplied result in +24 (the independent number of the equation)

• and when added or substracted result in -10 (the coefficient of the x in the equation)

In this case those 2 number are: -6 and -4 because:

(-6)(-4)=+24

-6 - 4 = -10

Thus we arrange our factored equation as follows:

from
`x^2-10x+24=0` through factoring we get:

`(x-6)(x-4)=0`

and because of the zero factor property (if two things when multiplied result in zero one of them or both must be zero), thus our x values are:

`x-6=0\\x=6\\`

and

`x-4=0\\x=4`

thus, our points are those with and y coordinate of 0 and an x coordinate of 6 and 4:

(4,0) and (6,0)