Question

The graph of f(x) = 2x^2 + 20x + 48 is shown

a. Write the equation in intercept form by factoring.


b. What are the x-intercepts of the graph?

What are the zeros of the function?

What are the roots of the function?


c. What are the solutions of 2x^2 + 20x + 48 = 0

Answer 1

a) The equation in intercept form by factoring is (x+6)(x+4)

b) From the given graph x- intercepts are (-4,0) and (-6,0) and zeros (roots) of the function are -6 and -4.

c) The solutions of
`2x^2+20x+48=0` is
`(x+6)(x+4)=0` that is x= -6 and x = -4.

Explanation:

The given quadratic equation is
`f(x)=2x^2+20x+48`

Put the function f(x) = 0 , then
`f(x)=2x^2+20x+48=0`

a) The equation in intercept form by factoring is ,

Consider the given function,

`f(x)=2x^2+20x+48=0`

`\Rightarrow 2x^2+20x+48=0`

taking 2 common, we get,

`\Rightarrow 2(x^2+10x+24)=0`

`\Rightarrow x^2+10x+24=0`

The above is a quadratic equation of the form
`ax^2+bx+c=0`

Solving quadratic equation using middle term splitting method,

`\Rightarrow x^2+6x+4x+24=0`

`\Rightarrow x(x+6)+4(x+6)=0`

`\Rightarrow (x+6)(x+4)=0`

Thus, The equation in intercept form by factoring is (x+6)(x+4).

b) From the given graph x- intercepts are (-4,0) and (-6,0) .

Zeroes / roots of a function are those points where the value of the function is zero.

Put f(x) = 0 as solved above

that is
`(x+6)(x+4)=0`

`\Rightarrow (x+6)=0` or
`\Rightarrow (x+4)=0`

`\Rightarrow x=-6` or
`\Rightarrow x=-4`

Thus, zeros (roots) of the function are -6 and -4.

For checking put x = -6 and -4 in the function we get f(x) =0 .

c) The solutions of
`2x^2+20x+48=0` is
`(x+6)(x+4)=0` that is x= -6 and x = -4 as shown above.