Question

Drag the tiles to the correct boxes to complete the pairs.

Match the graphs with the functions they represent.

Answer 1

Explanation:

Equation of a parabola with vertex (h, k) is given by,

y - k = a(x - h)²

Equation of a function 'f' with vertex (0, 3) will be,

y - 3 = a(x - 0)²

y - 3 = ax²

Since, graph of this function passes through (1, 4),

4 - 3 = a(1)²

a = 1

Therefore, equation will be,

y - 3 = (x - 0)²

f(x) = x² + 3

Equation of function 'g' with vertex at (0, -3) will be,

y - (-3) = a(x - 0)²

y + 3 = ax²

y = ax² - 3

Since, the graph passes through (1, -1),

-1 = a(1)² - 3

a = 2

Therefore, equation will be,

y = 2x²- 3

g(x) = 2x² - 3

Equation of the function 'j' with the vertex (0, -3) will be,

y - (-3) = a(x - 0)²

y + 3 = ax²

y = ax²- 3

Since, the graph of the function passes through (1, -5),

-5 = a(1)² - 3

a = -2

Therefore, function 'j' will be,

j(x) = -2x² - 3

Equation of the function 'h' with the vertex (0, -3) will be,

y - (-3) = a(x - 0)²

y + 3 = ax²

y = ax² - 3

Since, the graph of the function passes through (2, 1)

1 + 3 = a(2)²

4 = 4a

a = 1

Therefore, equation of the function 'h' will be,

h(x) = x² - 3