Find a Quadratic Maximum in SAT Testing Desmos

Enter y equals negative two x squared plus twelve x plus five. The original window can hide the maximum. Open Graph Settings. Set the x minimum to zero and maximum to six, and the y minimum to zero and maximum to twenty five. This window includes the allowed input interval and the top of the parabola. Changing the viewing window does not restrict the equation itself. Keep the question’s domain in mind.

Select the curve, then tap the vertex point. The displayed coordinates are three comma twenty three. Three is the input; twenty three is the maximum output. Completing the square gives negative two times x minus three squared, plus twenty three. A negative square cannot increase that value. The permitted interval contains three, and both endpoints give five. For a different interval, check its endpoints and whether the vertex is allowed.

−2x² + 12x + 5 = −2(x − 3)² + 23. On 0 ≤ x ≤ 6, the vertex at x = 3 is allowed and y = 23 is maximal. At x = 0 and x = 6, y = 5.

On 0 ≤ x ≤ 2, what is the maximum of the same model? The vertex x = 3 is outside that interval. The function is increasing there, so the maximum is y(2) = 21, not 23.

Enter y equals negative two x squared plus twelve x plus five. The original window can hide the maximum. Open Graph Settings. Set the x minimum to zero and maximum to six, and the y minimum to zero and maximum to twenty five. This window includes the allowed input interval and the top of the parabola. Changing the viewing window does not restrict the equation itself. Keep the question’s domain in mind.

Select the curve, then tap the vertex point. The displayed coordinates are three comma twenty three. Three is the input; twenty three is the maximum output. Completing the square gives negative two times x minus three squared, plus twenty three. A negative square cannot increase that value. The permitted interval contains three, and both endpoints give five. For a different interval, check its endpoints and whether the vertex is allowed.

The video presents actual calculator screen captures with Google-generated narration. It is a narrated sequence of captured steps. Captures were checked on October 13, 2026 in the College Board testing configuration. Captions are timed by the measured narration segments; sentence timings within a segment are approximate. Desmos and College Board do not endorse PeakSAT.