Determine the two equations necessary to graph the horizontal parabola using a graphing calculator.
-$$x = 8 y ^ { 2 } - 5 y + 7$$
A) $\mathrm { y } = \frac { 5 - \sqrt { 32 \mathrm { x } - 199 } } { 16 }$ and $\mathrm { y } = \frac { 5 + \sqrt { 32 \mathrm { x } - 199 } } { 16 }$
B) $y = \sqrt { \frac { x - 7 } { - 5 } }$ and $y = - \sqrt { \frac { x - 7 } { - 5 } }$
C) $\mathrm { y } = \frac { 5 - \sqrt { 32 \mathrm { x } - 199 } } { 8 }$ and $\mathrm { y } = - \frac { 5 + \sqrt { 32 \mathrm { x } - 199 } } { 8 }$
D) $y = \frac { \sqrt { x - 7 } } { - 5 }$ and $y = - \frac { \sqrt { x - 7 } } { - 5 }$

Question

Quizplus · Accepted Answer

To graph the given horizontal parabola $x = 8y^2 - 5y + 7$ on a graphing calculator, we need to solve for $y$ in terms of $x$. This involves completing the square or using the quadratic formula. The correct transformation of the equation into $y$ in terms of $x$ results in two functions, representing the upper and lower halves of the parabola. The correct equations are $\mathrm { y } = \frac { 5 - \sqrt { 32 \mathrm { x } - 199 } } { 16 }$ and $\mathrm { y } = \frac { 5 + \sqrt { 32 \mathrm { x } - 199 } } { 16 }$, which correctly solve the original equation for $y$, taking into account the quadratic nature of the relationship between $x$ and $y$.

Determine the Two Equations Necessary to Graph the Horizontal Parabola x=8y2−5y+7x = 8 y ^ { 2 } - 5 y + 7x=8y2−5y+7

Determine the Two Equations Necessary to Graph the Horizontal Parabola $x = 8 y ^ { 2 } - 5 y + 7$