Considering the definition of vertex, the vertex form of y = –3x² – 12x – 2 is y=a(x+2)²+10 , where (-2,10) is the vertex of the parabola.
The function f(x) = ax² + bx + c
with a, b, c real numbers and a ≠ 0, is a function quadratic expressed in its polynomial form (It is so called because the function is expressed by a polynomial).
The quadratic function can be expressed by the vertex form of a quadratic equation: y=a(x−h)²+k , where (h,k)= vertex of the parabola.
The formula to find the value x of the vertex of a quadratic equation is [tex]x=\frac{-b}{2a}[/tex]
To calculate the value of y of the vertex, it is necessary to find the numerical value of "x vertex" in the polynomial expression. This is:
(h,k)= ([tex]\frac{-b}{2a}[/tex], [tex]f(\frac{-b}{2a})[/tex])
In this case:
Replacing in the formula to find the value x of the vertex of a quadratic equation, you get:
[tex]x=\frac{-(-12)}{2(-3)}[/tex]
Solving:
[tex]x=\frac{12}{-6}[/tex]
x= -2
The value of y of the vertex can be calculated as:
y = –3×(-2)² – 12×(-2) – 2
Solving:
y= –3×4 – 12×(-2) – 2
y= –12 +24 – 2
y=10
Finally, the vertex form of y = –3x² – 12x – 2 is y=a(x+2)²+10 , where (-2,10) is the vertex of the parabola.
Learn more about vertex form of a cuadratic function:
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