Find the quadratic function that has vertex (10,-7) and whose graph goes through the point (3, 385)

y = 8x² - 160x + 793

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) = (10, - 7), hence

y = a(x - 10)² - 7

To find a substitute (3, 385) into the equation

385 = a(3 - 10)² - 7

385 = 49a - 7 ( add 7 to both sides )

392 = 49a ( divide both sides by 49 )

a = 8

y = 8(x - 10)² - 7 ← in vertex form

Expand the factors and simplify

y = 8(x² - 20x + 100) - 7

y = 8x² - 160x + 800 - 7

y = 8x² - 160x + 793 ← in standard form

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europa2433

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