Graph the function f(x)=7(x–4)^2+3.

Answer 1

To graph the function f(x) = 7(x – 4)^2 + 3, we can start by identifying key points and the general shape of the graph.

The vertex form of a quadratic function is given by f(x) = a(x – h)^2 + k, where (h, k) represents the vertex of the parabola. In this case, h = 4 and k = 3.

The vertex represents the lowest or highest point of the parabola, depending on the value of a. Since a = 7, the parabola opens upward.

First, let's plot the vertex (4, 3) on a coordinate plane:

Next, let's find the y-intercept by substituting x = 0 into the equation:
f(0) = 7(0 – 4)^2 + 3
f(0) = 7(16) + 3
f(0) = 112 + 3
f(0) = 115

The y-intercept is 115, so we can plot the point (0, 115) on the graph.

Now, let's find two other points on the graph to make it symmetrical. We can choose to substitute x = 1 and x = 7 into the equation:
f(1) = 7(1 – 4)^2 + 3
f(1) = 7(-3)^2 + 3
f(1) = 7(9) + 3
f(1) = 63 + 3
f(1) = 66

The point (1, 66) is another point on the graph.

f(7) = 7(7 – 4)^2 + 3
f(7) = 7(3)^2 + 3
f(7) = 7(9) + 3
f(7) = 63 + 3
f(7) = 66

The point (7, 66) is symmetric to (1, 66) about the vertex.

Using these points, we can sketch the graph of f(x):

The graph is a U-shaped parabola that opens upward and passes through the vertex (4, 3), the y-intercept (0, 115), and the symmetric points (1, 66) and (7, 66).

Answer 2

Complete the sentence with the correct comparative or superlative adverb.
My grandmother is always frustrated by her hearing aids; she claims she hears even with them in.

Which word goes after even?

Answer 3

The word that goes after "even" in this sentence is "worse." The complete sentence would be: "My grandmother is always frustrated by her hearing aids; she claims she hears even worse with them in."