Answer:
B) Graph B
Step-by-step explanation:
The quadratic equation in vertex form is represented by: y = a(x - h)² + k, where:
(h, k) = vertex
x = h : axis of symmetry
a = indicates a reflection in the x-axis; it also determines the graph's vertical stretch or shrink.
- a > 0 the graph opens up.
- a < 0: the graph opens down.
h = indicates a horizontal translation.
k = indicates a vertical translation.
Given the given quadratic equation, y = (x - 2)² - 16:
The vertex occurs at point, (2, -16), and a = 1. Since the value of a is positive, then it implies that the graph opens upward, and the vertex is its minimum point. The axis of symmetry occurs at h = 2.
To determine another point to use as a reference (and also for graphing) is solving for the equation's y-intercept, which is the point where it crosses the y-axis (where x = 0).
Y-intercept: set x = 0:
y = (x - 2)² - 16
y = (0 - 2)² - 16
y = (-2)² - 16
y = 4 - 16
y = -12
Therefore, the y-intercept is (0, -12).
Therefore, the graph that matches these given descriptions is Graph B.
Attached is the graphed quadratic equation where it shows the vertex, y-intercept, and the axis of symmetry.
