Question

Which function matches the graph?

A 2-dimensional graph with an x-axis and a y-axis is given. A parabolic curve is drawn whose axis of symmetry is parallel to y-axis and its vertex is at (1,-3); is passing through co-ordinates (3,1) and (-1,1).
A. f(x) = (x – 3)2 – 3
B. f(x) = (x + 1)2 – 6
C. f(x) = (x + 2)2 – 5
D. f(x) = (x – 1)2 – 3

Answer 1

Answer: Graph the parabola y=x2−7x+2 .

Compare the equation with y=ax2+bx+c to find the values of a , b , and c .

Here, a=1,b=−7 and c=2 .

Use the values of the coefficients to write the equation of axis of symmetry .

The graph of a quadratic equation in the form y=ax2+bx+c has as its axis of symmetry the line x=−b2a . So, the equation of the axis of symmetry of the given parabola is x=−(−7)2(1) or x=72 .

Substitute x=72 in the equation to find the y -coordinate of the vertex.

y=(72)2−7(72)+2 =494−492+2 =49 − 98 + 84  =−414

Therefore, the coordinates of the vertex are (72,−414) .

Now, substitute a few more x -values in the equation to get the corresponding y -values.

x y=x2−7x+2

0 2

1 −4

2 −8

3 −10

5 −8

7 2

Plot the points and join them to get the parabola

in short terms D.

Answer 2

vertex : (1,-3)

coordinates : (3,1) and (-1,1)

parabola formula : y = a(x -h)² + k

• (x, y) - from the coordinates

• (h, k) - from the vertex

so given,

h = 1

k = -3

x = 3

y = 1

solve for a:

• 1 = a(3 -1)² + (-3)

• 1 = 4(a) - 3

• 4(a) = 4

• a = 1

Therefore equation:

y = (x -1)² - 3

check the graph for confirmation: