Problem

A curved path is \(y=x^{2}\) and a ramp is \(y=3x+10\). Set the equations equal, factor the resulting quadratic, calculate both \(y\)-values rather than reusing the constant, interpret the points, and verify the displayed answer graph.

Answer choices

Choose your path.

Preview only

System: y = x² and y = 3x + 10. Set equal: x² = 3x + 10, so x² − 3x − 10 = 0. Inputs −2 and 5 give points (−2, 4) and (5, 25): the points are interpreted as x-intercepts.

System: y = x² and y = 3x + 10. Set equal: x² = 3x + 10, so x² − 3x − 10 = 0 = (x − 2)(x + 5). Inputs 2 and −5 give points (2, 4) and (−5, 25).

System: y = x² and y = 3x + 10. Set equal: x² = 3x + 10, so x² − 3x − 10 = 0. Inputs −2 and 5 give points (−2, 10) and (5, 10): both intersections are assigned the line constant.

System: y = x² and y = 3x + 10. Set equal: x² = 3x + 10, so x² − 3x − 10 = 0 = (x + 2)(x − 5). Inputs −2 and 5 give points (−2, 4) and (5, 25).

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

A curved path is \(y=x^{2}\) and a ramp is \(y=3x+10\). Set the equations equal, factor the resulting quadratic, calculate both \(y\)-values rather than reusing the constant, interpret the points, and verify the displayed answer graph.

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.