Answer:
y = x² - 6x + 10
Step-by-step explanation:
The equation of a quadratic 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) = (3, 1), thus
y = a(x - 3)² + 1
To find a substitute (0, 10) into the equation
10 = a (0 - 3)² + 1, that is
10 = 9a + 1 ( subtract 1 from both sides )
9 = 9a ( divide both sides by 9 )
a = 1, thus
y = (x - 3)² + 1 ← expanding and simplifying
y = x² - 6x + 9 + 1, that is
y = x² - 6x + 10
