Recall the vertex form a parabola:

y = a(x - h)^2 + k , where (h, k) is the vetex.

Therefore, the equation of the parabola is y = a x^2.

All, we have to do now is solve for a. Since we know that the point (8, -4) lies on the parabola,

8 = a (-4)^2 => a = 1/2.

Therefore, the equation of the parabola is y = 1/2 x^2.

I found an answer from www.khanacademy.com

**Vertex** & axis of symmetry of a **parabola** (video) | Khan Academy

Sal rewrites a quadratic **equation** in **vertex form** and shows how it reveals the ...
**through**. 6:10. Sal says "when x is equal to three it's also going to be equal to **8**" ...
he meant "when x is equal to **4**" because we are calling each line ... I get that the
**parabola** will open **upward** when a>**0** and **downward** when a<**0**, but what if a=**0**?

For more information, see **Vertex** & axis of symmetry of a **parabola** (video) | Khan Academy

I found an answer from www.quora.com

What's the **equation for** a **parabola** with a stretch factor of **4** and ...

What's the **equation for** a **parabola** with a stretch factor of **4** and **vertex** of (6, **0**)? ...
What is the **equation** of the **parabola** with x intercepts -**4** and 3 and that **passes**
**through** (-2,7)? ... How do I **write** the **equation** in any **form**? ... Latus rectum joining
the points (-**4**,2) and (2,1) with axis vertical and **opening up**? ... What is **its** focus?

For more information, see What's the **equation for** a **parabola** with a stretch factor of **4** and ...

I found an answer from answers.yahoo.com

A **parabola opening up** or **down has vertex** (**0**, – 3) and **passes** ...

Nov 19, 2020 **...** A **parabola opening up** or **down has vertex** (**0**, – 3) and **passes through** (10, – **8**).
**Write its equation** in **vertex form**. Simplify any fractions.?

For more information, see A **parabola opening up** or **down has vertex** (**0**, – 3) and **passes** ...

I found an answer from www.khanacademy.org

**Finding** the **vertex** of a **parabola** in standard **form** (video) | Khan ...

Sal rewrites the **equation** y=-5x^2-20x+15 in **vertex form** (by completing the
square) in order to identify the **vertex** of the corresponding **parabola**.

For more information, see **Finding** the **vertex** of a **parabola** in standard **form** (video) | Khan ...