Question

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

Answer 1

Answer:

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.

Step-by-step 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.