Question

I need help with 6-8

Answer 1

Answer:

6. y² = 169x

7. y² = 12x

8. $y^{2} = \frac{1}{2}x$

Step-by-step explanation:

The equation of a quadratic function in vertex form is given by  

(y - α)² = 4a(x - β)

Where, (α,β) is the vertex of the function and a is the distance from vertex to its focus.

6. Here, (α,β) ≡ (0,0) and a point on the equation is (1,13)

So, the equation will be y² = 4ax

⇒ 13² = 4a(1)  

⇒ 4a = 169

Therefore, the original equation will be y² = 169x  (Answer)

7. Here also the vertex is (0,0) and a point on the equation is (3,-6),

So, (-6)² = 4a(3)  

⇒ 4a = 12

So, the equation is y² = 12x (Answer)

8. Here also the vertex is (0,0) and a point on the equation is ($\frac{1}{2},\frac{1}{2}$),

So, $(\frac{1}{2})^{2} = 4a(\frac{1}{2})$

⇒ $4a = \frac{1}{2}$

So, the equation is $y^{2} = \frac{1}{2}x$ (Answer)