# Which equation is y = 3(x - 2)^{2} - (x - 5)^{2} rewritten in vertex form?

y = 3(x minus seven-halves) squared minus Start Fraction 27 Over 4 End Fraction

y = 2(x minus 1) squared minus 11

y = 2(x minus one-half) squared minus Start Fraction 53 Over 4 End Fraction

y = 2(x minus one-half) squared minus Start Fraction 27 Over 2 End Fraction

**Solution:**

The vertex form of the equation of a parabola is

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

Where (h, k) is the vertex of the parabola

It is given that

y = 3(x - 2)^{2} - (x - 5)^{2}

Using the algebraic identity (a - b)^{2} = a^{2} - 2ab + b^{2}

y = 3 (x^{2} - 4x + 4) - (x^{2} - 10x + 25)

y = 3x^{2} - 12x + 12 - x^{2} + 10x - 25

By further calculation

y = 3x^{2} - x^{2} - 12x + 10x + 12 - 25

y = 2x^{2} - 2x - 13

Taking out 2 as common

y = 2(x^{2} - x - 13/2)

Let us add and subtract 1/2

y = 2(x^{2} - x + 1/4 - 1/4 - 13/2)

y = 2 [(x - 1/2)^{2} - (1 + 26)/4]

So we get,

y = 2 [(x - 1/2)^{2} - 27/4]

y = 2 [(x - 1/2)^{2}] - 27/2

Therefore, the vertex form is y = 2 (x minus one-half) squared minus Start Fraction 27 Over 2 End Fraction.

## Which equation is y = 3(x - 2)^{2} - (x - 5)^{2} rewritten in vertex form?

**Summary:**

The equation y = 3(x - 2)^{2} - (x - 5)^{2} rewritten in vertex form is y = 2 (x minus one-half) squared minus Start Fraction 27 Over 2 End Fraction.

visual curriculum