Answer: (4, -1) -- All real numbers -- [-1, ∞) -- (3,0) and (5,0). -- (0,15) -- x = 4 -- y = x^2-8x+15
Explanation:
a) Vertex: (4, -1). In a quadratic in vertex form:
, the vertex is the point (h,k)
b) Domain: Since it is a valid quadratic function, the graph extends for all x values. (in other words, you can plug in any value for x). The domain is thus all real numbers.
c) Range: You can plug in any value for x, but since x is being squared, you wont get every value out, you will only get positives out. But there is another condition; there is a -1 constant trailing the equation. this means the graph is shifted one unit down. thus, the y values, the range, is taken down by one as well. the range is thus all numbers from -1 to ∞, or in interval notation, [-1, ∞)
d) X-intercepts: from the graph we can see the intercepts are (3,0) and (5,0).
e) Also from the graph, the y-intercept can be seen as: (0,15)
f) Axis of Symmetry: It is always the line x = x-coordinate of vertex.
so in this case, the line will be x = 4
g) to find a congruent equation, simply expand this equation:
there ya go!