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) = (9, 7), thus
y = a(x - 9)² + 7
To find a substitute (3, 8) into the equation
8 = a(3 - 9)² + 7
8 = 36a + 7 ( subtract 7 from both sides )
36a = 1 ( divide both sides by 36 )
a = [tex]\frac{1}{36}[/tex]
y = [tex]\frac{1}{36}[/tex](x - 9)² + 7 ← in vertex form
Expanding the factor and simplifying
y = [tex]\frac{1}{36}[/tex](x² - 18x + 81) + 7
= [tex]\frac{1}{36}[/tex] x² - [tex]\frac{1}{2}[/tex] x + [tex]\frac{9}{4}[/tex] + 7
= [tex]\frac{1}{36}[/tex] x² - [tex]\frac{1}{2}[/tex] x + [tex]\frac{37}{4}[/tex] ← in standard form
