Question

The vertex of the graph of a quadratic function is (3, 1) and the y-intercept is (0, 10). Which of the following is the

equation of the function?
A. y = 2x² - 12x + 10
B. 1, 11
= --x + 3x - -
2
y=x2 - 6x +10
D. y = 2x? - 7x+4
Please select the best answer from the choices provided

Answer 1

y = x² - 6x + 10

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