Question 1189918
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The graph of a certain quadratic y = ax^2 + bx + c is a parabola with vertex (-4,0) 
which passes through the point (1,-75). What is the value of a?
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            Hello, you do not need make all these calculations and transformations,

            which @MathLover1 makes in her post.


            The solution is in couple of lines below.



<pre>
You are given that a quadratic function is a parabola with vertex (-4,0).


It means that the function in vertex form is  

    y = a*(x-(-4))^2 + 0 = a*(x+4)^2.      (1)


The only unknown is the parameter "a". To find it, use the given part, which says
that the parabola passes through the point (1,-75).


So, at x= 1 the value of the function (1) should be -75.  You write this equation, based on (1)

    -75 = a*(1+4))^2,  or  -75 = a*5^2,  which is  25a = -75.


From this equation,  a = {{{-75/25}}} = -3.   


<U>ANSWER</U>.  The value of "a" is  -3.
</pre>

Solved.