Question 1:
For this case we have:
The value of the x coordinate of the vertex is with the equation given by:
[tex]x = -\frac{b}{2a} \\[/tex]
Where b = -12 and a = -1
therefore,
[tex]x =- \frac{-12}{2(-1)} \\\\x = -6\\[/tex]
To find the coordinate and substitute in the equation:
[tex]y = - (- 6) ^ 2-12 (-6) -32\\\\y = 4\\[/tex]
Answer:
The coordinates of the vertex are (-6.4)
Question 2:
For this case we have the following equation:
[tex]y = -x ^ 2 - 12x - 32\\[/tex]
By definition, to find the intercept point with the y axis, we make x = 0 and substitute as shown below:
[tex]y = - (0) ^ 2-12 (0) -32\\\\y = -32\\[/tex]
Thus, the intercept point with the y axis is given by (0, -32)
Answer:
the y-intercept is (0, -32)
Question 3:
For this case we have the following equation:
[tex]y = -x ^ 2 - 12x - 32\\[/tex]
The zeros of the function are given by the cut points with the x axis, so, equaling the equation to zero and clearing x we have:
[tex]0 = -x ^ 2 - 12x - 32\\[/tex]
Rewriting the equation we have:
[tex]0 = x ^ 2 + 12x +32\\[/tex]
Factoring has the following:
[tex](x + 4) (x + 8) = 0\\[/tex]
Thus, the solutions are given by:
[tex]x = -4 \\\\x = -8\\[/tex]
Therefore, the zeros of the equation are (-4.0) and (-8.0)
Answer:
(-4.0) and (-8.0)
