Find the standard equation of any parabola that has vertex V. V(−3,1)

Question

Find the standard equation of any parabola that  has vertex V.  V(−3,1)

Delorenzoz · Accepted Answer

Step 1
The equation is a statement that consists of equal symbol between two algebraic expressions. The solution for the variable of the equation must satisfy the equation when we resubstitute the solution in the equation.
Step 2
Quadratic equations are the polynomial equations of degree 2 in one variable of type

f (x) = a x^{2} + b x + c

where a, b, c, are real values and

a \neq 0

. The equation of a parabola is a quadratic equation. Let it be as

y = a x^{2} + b x + c

. To get the standard form of parabola equation with vertex at (-3, 1) substitute this point in the vertex equation of parabola and simplify it to write it in standard form as follows;
The parabola equation with vertex at (h, k) is

y = a {(x - h)}^{2} + k

.
So, substitute the given vertex point (-3, 1) in the vertex equation of parabola with

(h, k) = (- 3, 1)

as follows;

y = a {(x - h)}^{2} + k

y = a {(x - (- 3))}^{2} + 1

............. Substitute the vertex

(h, k) = (- 3, 1)

.

y = a {(x + 3)}^{2} + 1

= a (x^{2} + 6 x + 9) + 1

= a x^{2} + 6 a x + 9 a + 1

Hence, the standard equation of the parabola with the vertex at (-3, 1) is

y = a x^{2} + 6 a x + 9 a + 1

, where a is non-zero real number.

Find the standard equation of any parabola that has vertex V. V(-3,1)

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