y = −x^2+3x−7

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on Mar 30, 2025 at 1:46 am



You asked:

Investigate the equation: y=−x2+3x−7y = -{x}^{2} + 3 x - 7.

MathBot Answer:

The graph of the equation y=−x2+3x−7y = -{x}^{2} + 3 x - 7 is a parabola.

The coordinates of its vertex are: (32,−194)\left(\frac{3}{2}, - \frac{19}{4}\right)

The coordinates of its focus are: (32,−5)\left(\frac{3}{2}, -5\right)

The directrix has equation: −4y−18=0- 4 y - 18 = 0.

The parabola has parameterization: x(θ)=32+θy(θ)=−194−θ2\begin{aligned}x\left(\theta\right) &= \frac{3}{2} + \theta\\y\left(\theta\right) &= - \frac{19}{4} - \theta^{2}\end{aligned}
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