Graph the quadratic function. Plot the vertex and anyintercepts. f ( x ) = ( x 2

Question

Graph the quadratic function. Plot the vertex and anyintercepts.

f(x) = (x 2)2 +6

STEP1:

Identify the vertex of theparabola.
(x, y) = ( 1, 2)

STEP2:

Identify the y-interceptof the parabola.
(x, y) = ( 3, 4)

STEP3:

How many x-intercepts are there?

5

0
1
2

STEP4:

Identify the axis of symmetry.
x =

6

STEP1:

Identify the vertex of theparabola.
(x, y) = ( 1, 2)

STEP2:

Identify the y-interceptof the parabola.
(x, y) = ( 3, 4)

STEP3:

How many x-intercepts are there?

5

0
1
2

STEP4:

Identify the axis of symmetry.
x =

6

Explanation / Answer

The vertex form of the quadratic is   y = (x - h)2 + k,   where the point ( h , k ) is thelocation of the vertex. In this case, the vertex is at ( 2, 6 ). The y-intercept occurs when x = 0.   Thus, they-intercept is   ( 0 - 2)2 +6  =   4.      y-intercept =4. There are NO x-intercepts. Graph the given eqn and youwill not see any x-intercepts at all. The axis of symmetry occurs at   x = - b /2a.   To see the values of a and b, we have to put thegiven quadratic in standard form like   y =ax2 + bx + c. Our eqn is y = x2 - 4x +10,   so a= 1,   and b = -4.           x =- b / 2a = +4 / 2 = 2. Axis of symmetry isx = 2.

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