A toy rocket is shot up into the air and this is modeled by the function: y=-16x^2+145x+7, Find the vertex and find the zeros of the equation and state whether or not each one is realistic. Show or explain how you found your answer.

Vertex (4.53 , 335.33) Zeroes are -0.048 and 9.11

Step-by-step explanation:

For find the Vertex also know as the turning point/stationary point and the zeros also known as the x-intercepts of the equation we equate the equation to its complete square form which is

where (h,k) are the vertex point of the equation h corresponds to x coordinate and k corresponds to the y coordinate and a determines whether the graph is a maximum or a minimum. To find whether the graph is a maximum value of a should be < 0 which and if a's value is > 0 then the graph is a minimum. In short

maximum (n shaped)

minimum (u shaped

so now we equate, that is

now we compare the coefficients of x^2

-

now we compare the coefficients of x

now we compare constants

so now we the value of (h , k) that is (4.53 , 335.33)

that is our vertex and since the value of a is less than zero the graph is a maximum.

Now for the zeroes/x-intercepts

we need to find where the graph cuts the x-axis which means if the specific point where the curve cuts the x-axis that point's y coordinate should be zero or more like .

and thus this point lies on the curve/equation as well because it satisfies it which means we can put this point into our given equation

when we put in it y becomes 0 thus changing it to

this becomes a simple quadratic equation where we can use the quadratic formula

±

we get two values of x

and

      and since there 2 values of x means the curve cuts the x-axis at two points we can even confirm our answers by using the desmos graphing calculator as well to check our vertex and zeroes.

is there answer choices?