Question

Compare the graph of m(x) = 0.7x² + 4 with the graph of n(x) = x².

Answer 1

Answer:

B.) The graph of m(x) is wider.

     Both graphs open upward.

     Both have the axis of symmetry x = 0.

     The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).

Step-by-step explanation:

When the coefficient before x² is greater than 1, the curve of the graph is narrower. When the coefficient is less than 1, the curve of the graph is wider.

When the coefficient in front of x² is positive, the graph opens upwards. When the coefficient is negative, the graph opens downwards.

The axis of symmetry is the "x" value which divides the curve into two equal sections. Their axis of symmetry are both x = 0 because their vertexes (the lowest point of the curve) are both at x = 0.

The vertex can be found by plugging x = 0 into both of the equations and then solving. The resulting value is the "y" position of the vertex.

m(0) = 0.7(0)² + 4                        n(0) = (0)²

m(0) = 0 + 4                                 n(0) = 0

m(0) = 4

Therefore, the vertexes are m(x) =  (0,4) and n(x) = (0,0).

Answer 2

Answer:

Step-by-step explanation:

m(x) =.7x^2 + 4

n(x) = x^2

In the graph below

green = m(x)

blue = n(x)

Answer:

• Just look at the graph below
• Both graphs open upward.
• The vertex of m(x) is (0, 4); the vertex of n(x) is (0, 0).
• The graph of m(x) is wider.