Use the vertex \left(h, k\right) and a point on the graph N

Carol Gates

Carol Gates

Answered question

2021-10-30

Use the vertex
(h,k)
and a point on the graph
(x,y)
to find the general form of the equation of the quadratic function.
(h,k)=(0,3), (x,y)=(1,4)
f(x)=?

Answer & Explanation

d2saint0

d2saint0

Skilled2021-10-31Added 89 answers

The vertex and pointa are:
(h,k)=(0,3), (x,y)=(1,4)
The standard form of the quadratic equation is:
y=a(xh)2+k
Substitute the values of vertex:
y=a(x0)2+3
y=ax2+3
Substitute the values of points in this equation to find a:
4=a(1)2+3
a(1)2+3=4
a+3=4
a=43
A=1
On substituting the value of a, the equation is,
y=x2+3
This is the equation in general form of the form,
y=ax2+bx+c
where a=1, 6=0, c=3

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