The quadratic function which has zeros −3 and 5 and contains the point (4, 14) is 2x²+4x+30 and the vertex points are (-1,28).
<h3>What is a quadratic equation?</h3>
A quadratic equation is the equation in which the unknown variable is one and the highest power of the unknown variable is two.
The standard form of the quadratic equation is,
ax²+bx+c=0
Here,(a,b, c) is the real numbers and (x) is the variable.
A quadratic function has zeros −3 and 5 and contains the point (4, 14). The factored form of quadratic equation is,
f(x)=a(x-z₁)(x-z₂)
Here, z₁ and z₂ are the zeros. Thus,
f(x)=a(x-z₁)(x-z₂)
f(x)=a(x-(-3))(x-5)
f(x)=a(x+3)(x-5)
This equation contains the point (4,14). Thus,
14=a(4+3)(4-5)
14=a(7)(-1)
a=14/-7
a=-2
Put the value in above equation and solve it further:
f(x)=-2(x+3)(x-5)
f(x)=-2(x²-5x+3x-15)
f(x)=-2x²-4x-30
Change the sign,
f(x)=2x²+4x+30
The equation of the quadratic function in standard form is,
f(x)=2(x+1)²+28
Thus, the vertex point are -1 and 28. Similarly, the section equation which contains the point (1, −48) can be solved.
Hence, the quadratic function which has zeros −3 and 5 and contains the point (4, 14) is 2x²+4x+30 and the vertex points are (-1,28).
Learn more about the quadratic equation here;
brainly.com/question/1214333
#SPJ1
