Question 1180533
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Determine the x-intercept and vertex for this equation:
y = (x - 3)(x + 5)
*can work be shown please for understanding
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<pre>
You have a quadratic finction, presented as the product of two linear binomials.


The x-intercepts are the zeroes of these binomials.


One x-intercept  x= 3  comes as the zero of the binomial (x-3).


The other x-intercept  x= -5  comes as the zero of the binomial (x+5).



The x-coordinate of the vertex is exactly half-way between the x-inercepts  {{{x[vertex]}}} = {{{(3 - 5)/2}}} = {{{-2/2}}} = -1.


The y-coordinate of the vertex is the value of the given quadratic function at x= {{{x[vertex]}}} = -1.


So,  {{{y[vertext]}}} = (-1 -3)*(-1+5) = -4*4 = -16.


The coordinates of the vertex are  ({{{x[vertex]}}},{{{y[vertex]}}} = (-1,-16).


                          The plot



    {{{graph( 400, 400, -10, 10, -20, 20,        
              (x - 3)(x + 5)
)}}}


              The plot  y = (x - 3)(x + 5).
</pre>

Solved.