Answer:
[tex]\boxed{\text{B. 13}}[/tex]
Step-by-step explanation:
1. Find the equation of the parabola
The vertex is at (0, 0), so the axis of symmetry is the y-axis.
The graph passes through (7, 7), so it must also pass through (-7,7).
The vertex form of the equation for a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
If the vertex is at (0, 0),
h = 0 and k = 0
The equation is
y = ax²
2. Find the value of a
Insert the point (7,7).
7 = a(7)²
1 = 7a
a = ⅐
The equation in vertex form is
y = ⅐x²
3. Calculate the length of the segment when y = 6
[tex]\begin{array}{rcl}6 & = & \dfrac1{7}x^{2\\\\42 & = & x^{2\\x & = & \pm \sqrt{42}\\\end{array}[/tex]
The distance between the two points is the length (l) of line AB.
A is at (√42, 6); B is at (-√42, 6).
l = x₂ - x₁ = √42 – (-√42) = √42 + √42 = 2√42 ≈ 2 × 6.481 ≈ 13.0
[tex]\text{The length of the segment joining the points of intersection is }\boxed{\mathbf{13.0}}[/tex]
