Question

quiz 4.1.1 - quadratic graphs
< 2 of 2 1 2
a. (-3.4,0)
b. (5.4,0)
c. (2,4)
d. (4,2)

Explanation:

Step1: Identify x-intercepts

The quadratic graph crosses the x-axis at one visible point near x=3, and the other is the option we need to verify.

Step2: Analyze vertex and symmetry

The vertex (maximum point) is at (4,2) (from the graph's peak). The axis of symmetry is $x=4$.

Step3: Use symmetry formula

For a quadratic, if one x-intercept is $x_1$, the other $x_2$ satisfies $\frac{x_1+x_2}{2}=4$. The visible intercept is $x_1\approx2.6$.
$x_2 = 2\times4 - 2.6 = 5.4$
So the x-intercept is (5.4,0).

Answer:

b. (5.4,0)