Question

what will be the graph for the equation 6x-2x square +7. ??
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Answer 1

a downward parabola

$y = - 2 {x}^{2} + 6x + 7 \\ = > y = - 2 {(x - \frac{3}{2} )}^{2} + \frac{5}{2}$

Answer 2

(x - 1.5)² = - 0.5(y + 2.5)

Step-by-step explanation:

The given equation is y = 6x - 2x² + 7.

Rearranging the equation into vertex form of parabola equation as

y = -(2x² - 6x + 7)

⇒ y = - 2(x² - 3x + 3.5)

⇒ x² - 3x + 3.5 = - 0.5y

⇒ (x - 1.5)² - 1.5² + 3.5 = - 0.5y

⇒ (x - 1.5)² = 2.25 - 3.5 - 0.5y

⇒ (x - 1.5)² = - 0.5(y + 2.5)

Now, this is an equation of a parabola whose axis of symmetry is parallel to y-axis and opens to the negative y direction and it has vertex at (1.5, -2.5) and the equation of the axis is x = 1.5. (Answer)