Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (- 2, 2), thus
y = a(x + 2)² + 2
To find a substitute the point on the graph (0, 0) into the equation
0 = a(0 + 2)² + 2
0 = 4a + 2 ( subtract 2 from both sides )
- 2 = 4a ( divide both sides by 4 )
- [tex]\frac{1}{2}[/tex] = a
y = - [tex]\frac{1}{2}[/tex](x + 2)² + 2 ← in vertex form
Expanding and simplifying gives
y = - [tex]\frac{1}{2}[/tex](x² + 4x + 4) + 2
= - [tex]\frac{1}{2}[/tex]x² - 2x - 2 + 2
= - [tex]\frac{1}{2}[/tex]x² - 2x ← in standard form
