Parabolas: Video e Problemi di Pratica

Choose the correct option for the vertex, directrix, focus, and graph of the parabola.

(x +9)² = - 16(y + 3)

Choose the correct option for the vertex, directrix, focus, and graph of the parabola. 

(y - 9)² = -16(x - 3)

Using the provided equation, find the parabola's vertex, focus, and directrix. Then, graph the parabola.

(x - 7)² = 12(y - 3)

By graphing the given system in the same rectangular coordinate system and finding the intersection points, find the solution set and verify the solution.

y = x² +11

y = x² -11x

By graphing the given system in the same rectangular coordinate system and finding the intersection points, find the solution set and verify the solution.

y = (x -9)² -7

(x -9)² + (y -10)² = 9

Using the provided equation, find the parabola's vertex, focus, and directrix. Then, graph the parabola.

(x + 5)² = - 12(y + 2)

Using the provided equation, find the parabola's vertex, focus, and directrix. Then, graph the parabola.

(y + 8)² = 8(x + 6)

Using the provided equation, find the parabola's vertex, focus, and directrix. Then, graph the parabola.

(y + 9)² = - 4x

By completing the square, write the given equation into the standard form, and then identify the vertex, focus, and directrix of the parabola. Also, graph the parabola in a rectangular coordinate system.

x² - 4x - 4y +16 =0

By completing the square, write the given equation into the standard form, and then identify the vertex, focus, and directrix of the parabola. Also, graph the parabola in a rectangular coordinate system.

y² - 6y + 8x +41 = 0

By completing the square, write the given equation into the standard form, and then identify the vertex, focus, and directrix of the parabola. Also, graph the parabola in a rectangular coordinate system.

x² + 10x - 12y + 13 = 0

By graphing the given system in the same rectangular coordinate system and finding the intersection points, find the solution set and verify the solution.

(y-7)² = x +19

y = x -4

For the parabola $-12(y+4)=(x-3{)}^2$, find the $x$-coordinate of the vertex.

Find the value of $p$ for the parabola $16(y-5)=(x+2{)}^2$.

For the parabola $4(y-1)=(x+6{)}^2$, find the $y$-coordinate of the focus.

For the parabola $(y+1{)}^2=-20(x-4)$, determine the $x$-value of the directrix line $x=c$.

For the parabola $(x-2{)}^2=12(y+1)$, find the $x$-coordinate of the left width point (the width point with the smaller $x$-value).

Rewrite $y^2-8y-12x+4=0$ in the standard form of a parabola, and find the value of $p$.

For the parabola $(x+2{)}^2=-16(y-5)$, find the value of $p$.

For the parabola $(x+4{)}^2=20(y-1)$, the directrix has the form $y=c$. Find $c$.

Rewrite $y=-\frac{1}{8}{x}^2+x-4$ into the conic standard form $(x-h{)}^2=4p(y-k)$, then find $p$.