Question

Somebody please help me. . .  A graph of a quadratic function is shown below. Which of the following equations represents the axis of symmetry for the parabola shown? y = 10x x = 10 x = y + 10 y = x + 10

Answer 1

Option b

x=10 is axis of symmetry

Explanation:

Given is a parabola graph.

The parabola is open down with vertex as

(10,750)

From the parabola we can make out the parabola is symmetrical about the vertical line passing through the vertex

Any vertical line in two dimensional geometry would be of the form

x=a form

Since the axis of symmetry is a vertical line passing through (10,750)

we get the axis of symmetry is

x=10

Hence we have option b is the right answer

Answer 2

Before being able to find the equation for the axis of symmetry, let's find the equation of the parabola first. These are the general froms of equation for any given parabola:

(x-h)² = +/-4a (y-k) or (y-k)² = +/-4a(x-h)
where
(h,k) is the vertex of the parabola
a is the distance from the focus to the vertex

For parabolas intersecting the x-axis twice and facing downwards, the general form would be: (x-h)² = -4a (y-k)

Based on the given graph, the coordinates of the vertex is at (10, 790). Thus, h = 10 and k = 790. To find the value of a, substitute any point that is along the parabola. Let's choose (0,600). We use these x and y coordinates to substitute to the general form.

(0-10)² = -4a (600-790)
4a = 0.526
So, the equation of the parabola is

(x-10)² = -0.526(y-790)
Expanding the equation
x² - 20x + 100 = -0.526y + 415.54
x² - 20x + 100 - 415.54 = -0.526y
y = (x² - 20x - 315.54)÷-0.526
y = -1.9x² + 38.02x - 600

Let y be zero:
-1.9x² + 38.02x - 600 = 0

Now, this will be the basis for the equation of our axis of symmetry. From the general form of ax² + bx + c, the equation for axis of symmetry is x = -b/2a. From the given general form, a = -1.9 and b = 38.02. So, the axis of symmetry is

x = -38.02/2(-1.9)
x = 10

Technically, you really don't have to go through the solution. If you are given a graph, the axis of symmetry is the line that divides that parabola into halves as they intersect the vertex. Since the vertex is along x=10, the equation is x=10.