MATH SOLVE

4 months ago

Q:
# A parabola with a vertical axis has its vertex at the origin and passes through point (7,7). The parabola intersects line y = 6 at two points. The length of the segment joining these points isA. 14B. 13C. 12D. 8.6E. 6.5

Accepted Solution

A:

Answer:[tex]\boxed{\text{B. 13}}[/tex]Step-by-step explanation:1. Find the equation of the parabolaThe 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 isy = a(x - h)Β² + kwhere (h, k) is the vertex of the parabola.If the vertex is at (0, 0), Β h = 0 and k = 0The equation isy = axΒ²2. Find the value of aInsert the point (7,7).7 = a(7)Β²1 = 7aa = β
The equation in vertex form isy = β
xΒ²3. 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 (β42, 6); B is at (-β42, 6).
l = xβ - xβ = β42 β (-β42) = β42 + β42 = 2β42 β 2 Γ 6.481 β 13.0
[tex]\text{The length of the segment joining the points of intersection is }\boxed{\mathbf{13.0}}[/tex]