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Evgen [1.6K]
3 years ago
13

Rewrite the function in standard form, intercept form, find the vertex, find the y-intercept, and find the x-intercepts.

Mathematics
1 answer:
jasenka [17]3 years ago
8 0

Answer:

We have the function, f(x)=(x+3)^{2}-4

On simplifying, we get,

f(x)=x^2+6x+9-4

i.e. f(x)=x^2+6x+5

Thus, the standard form of the function is f(x)=x^2+6x+5.

Now, the factors of the given functions are (x+1) and (x+5).

<em>Since, the intercept form of the function is the factored form of the function.</em>

So, we have, intercept form of the function is f(x)=(x+1)(x+5).

Now, we know that,

Value of x-coordinate of the vertex is \frac{-b}{2a} i.e. \frac{-6}{2\times 1} i.e. \frac{-6}{2} i.e. x= -3

Then, f(-3)=(-3)^2+6\times (-3)+5 i.e. f(-3)=9-18+5 i.e. f(-3)=-4

So, the vertex of the function is (-3,-4).

Further, we know that,<em> 'the y-intercept of a function is the point where the function crosses y-axis'.</em>

So, when x=0, we have, f(0)=0^2+6\times 0+5 i.e. f(0) = 5

Thus, the y-intercept is (0,5)

Also, <em>'the x-intercept of a function is the point where the function crossese x-axis'.</em>

Then, for f(x)=0, we have 0=x^2+6x+5 i.e. 0=(x+1)(x+5) i.e. x= -1 and x= -5

Thus, the x-intercept are (-1,0) and (-5,0).

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