Question

Determine the direction of the parabola by the value a.

Answer 1

if a > 0, the direction of the parabola open up

option C

Step-by-step explanation

Given that;

`y\text{ -x}^2\text{ }+\text{ 2x = 2}`

Recall, that the standard form of parabola equation is written below as

`\text{ y }=\text{ a\lparen x - h\rparen}^2\text{ }+\text{ k}^2`

Where (h, k) are the vertex of the equation

Re-write the given equation into the general form of a parabola equation

`\begin{gathered} y\text{ - x}^2\text{ }+\text{ 2x }=\text{ 2} \\ y\text{ }=\text{ 2 - 2x }+\text{ x}^2 \\ y\text{ }=\text{ x}^2\text{ - 2x }+\text{ 2} \\ \text{ y }=\text{ \lparen x - 1\rparen}^2\text{ }+\text{ 1} \end{gathered}`

`\text{ y = \lparen x - 1\rparen}^2\text{ }+\text{ 1}`

Hence a is 1

Since a = 1, therefore a > 0

So, the correct answer is, if a > 0, the direction of the parabola open up

option C