Question

Which equation is y = –3x2 – 12x – 2 rewritten in vertex form? y = –3(x 2)2 10 y = –3(x – 2)2 10 y = –3(x 2)2 – 14 y = –3(x – 2)2 – 2

Answer 1

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.

Vertex form

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 $x=\frac{-b}{2a}$

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)=  ($\frac{-b}{2a}$, $f(\frac{-b}{2a})$)

Vertex form of y = –3x² – 12x – 2

In this case:

• a= -3
• b= -12
• c= -2

Replacing in the formula to find the value x of the vertex of a quadratic equation, you get:

$x=\frac{-(-12)}{2(-3)}$

Solving:

$x=\frac{12}{-6}$

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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