Respuesta :
Answer:
[tex]y=4x^2+8x-12[/tex]
Step-by-step explanation:
we know that
The quadratic equation in vertex form is equal to
[tex]y=a(x-h)^2+k[/tex]
where
a is the leading coefficient
(h,k) is the vertex of the quadratic equation
Remember that
In a quadratic equation the turning point is the same that the vertex
so
(h,k)=(-1,-16)
substitute
[tex]y=a(x+1)^2-16[/tex]
we have one zero at (-3,0)
substitute and solve for a
[tex]0=a(-3+1)^2-16[/tex]
[tex]0=4a-16\\4a=16\\a=4[/tex]
substitute
[tex]y=4(x+1)^2-16[/tex]
Convert to standard form
[tex]y=4(x^2+2x+1)-16\\y=4x^2+8x+4-16\\y=4x^2+8x-12[/tex]
The quadratic equation in standard form having one zero is at -3 and vertex at (-1, -16) is [tex]\rm y = 4(x+1)^2 -16[/tex].
What is a quadratic equation?
It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.
The equation of a quadratic function, in standard form, has one zero of -3 and a turning point at (-1,-16).
We know that the equation of quadratic equation is given as
[tex]\rm y = a(x-h)^2 + k[/tex]
Where a is a leading coefficient and (h, k) is the coordinate of the vertex.
The coordinate of the vertex is (-1, -16). Then we have
[tex]\rm y = a(x+1)^2 -16[/tex]
And one zero is at -3. Then we have
[tex]\rm 0 \ \ = a(-3+1)^2 -16\\\\16= a(-2)^2 \\\\a \ \ = 4[/tex]
Then the equation will be
[tex]\rm y = 4(x+1)^2 -16[/tex]
More about the quadratic equation link is given below.
https://brainly.com/question/2263981
