Math / Geometry

Question4. The points $(-3,8)$ and $(9,8)$ lie on opposite sides of a parabola. Determine the equation of the axis of symmetry.

Studdy Solution

STEP 1

What is this asking? Find the line that splits the parabola perfectly in half, given two points on opposite sides of it. Watch out! Don't assume the points are the vertex of the parabola!
They're just on opposite sides.

STEP 2

1. Find the x-coordinate of the vertex.
2. Write the equation of the axis of symmetry.

STEP 3

The axis of symmetry goes right through the vertex of a parabola.
Since our points are on opposite sides, the x-coordinate of the vertex is exactly halfway between the x-coordinates of our given points.
Think of it like balancing a seesaw!

STEP 4

To find the midpoint between two x-coordinates, we add them together and divide by $\bf{2}$ .
It's like finding the average!
We have $\bf{(-3)}$ and $\bf{9}$ .
$\frac{(-3) + 9}{2} = \frac{6}{2} = \bf{3}$

STEP 5

So, the x-coordinate of our vertex is $\bf{3}$ !

STEP 6

The axis of symmetry is a vertical line, and its equation always looks like $x = \text{something}$ .

STEP 7

We just found that the x-coordinate of the vertex is $\bf{3}$ .
This means the equation of our axis of symmetry is $x = 3$ .
Boom!

STEP 8

The equation of the axis of symmetry is $x = 3$ .

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Question4. The points $(-3,8)$ and $(9,8)$ lie on opposite sides of a parabola. Determine the equation of the axis of symmetry.

Studdy Solution

STEP 1

What is this asking? Find the line that splits the parabola perfectly in half, given two points on opposite sides of it. Watch out! Don't assume the points are the vertex of the parabola!
They're just on opposite sides.

STEP 2

1. Find the x-coordinate of the vertex.
2. Write the equation of the axis of symmetry.

STEP 3

The axis of symmetry goes right through the vertex of a parabola.
Since our points are on opposite sides, the x-coordinate of the vertex is exactly halfway between the x-coordinates of our given points.
Think of it like balancing a seesaw!

STEP 4

To find the midpoint between two x-coordinates, we add them together and divide by $\bf{2}$ .
It's like finding the average!
We have $\bf{(-3)}$ and $\bf{9}$ .
$\frac{(-3) + 9}{2} = \frac{6}{2} = \bf{3}$

STEP 5

So, the x-coordinate of our vertex is $\bf{3}$ !

STEP 6

The axis of symmetry is a vertical line, and its equation always looks like $x = \text{something}$ .

STEP 7

We just found that the x-coordinate of the vertex is $\bf{3}$ .
This means the equation of our axis of symmetry is $x = 3$ .
Boom!

STEP 8

The equation of the axis of symmetry is $x = 3$ .

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Question4. The points (−3,8)(-3,8)(−3,8) and (9,8)(9,8)(9,8) lie on opposite sides of a parabola. Determine the equation of the axis of symmetry.

Studdy Solution

STEP 1

What is this asking? Find the line that splits the parabola perfectly in half, given two points on opposite sides of it. Watch out! Don't assume the points are the *vertex* of the parabola!They're just on opposite sides.

STEP 2

1. Find the x-coordinate of the vertex.2. Write the equation of the axis of symmetry.

STEP 3

The axis of symmetry goes right through the vertex of a parabola.Since our points are on opposite sides, the x-coordinate of the vertex is exactly halfway between the x-coordinates of our given points.Think of it like balancing a seesaw!

STEP 4

To find the midpoint between two x-coordinates, we **add** them together and **divide** by 2\bf{2}2.It's like finding the average!We have (−3)\bf{(-3)}(−3) and 9\bf{9}9.(−3)+92=62=3 \frac{(-3) + 9}{2} = \frac{6}{2} = \bf{3} 2(−3)+9​=26​=3

STEP 5

So, the x-coordinate of our vertex is 3\bf{3}3!

STEP 6

The axis of symmetry is a vertical line, and its equation always looks like x=somethingx = \text{something}x=something.

STEP 7

We just found that the x-coordinate of the vertex is 3\bf{3}3.This means the equation of our axis of symmetry is x=3x = 3x=3.Boom!

STEP 8

The equation of the axis of symmetry is x=3x = 3x=3.

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question4. The points $(-3,8)$ and $(9,8)$ lie on opposite sides of a parabola. Determine the equation of the axis of symmetry.

What is this asking? Find the line that splits the parabola perfectly in half, given two points on opposite sides of it. Watch out! Don't assume the points are the vertex of the parabola!
They're just on opposite sides.

1. Find the x-coordinate of the vertex.
2. Write the equation of the axis of symmetry.

The axis of symmetry goes right through the vertex of a parabola.
Since our points are on opposite sides, the x-coordinate of the vertex is exactly halfway between the x-coordinates of our given points.
Think of it like balancing a seesaw!

To find the midpoint between two x-coordinates, we add them together and divide by $\bf{2}$ .
It's like finding the average!
We have $\bf{(-3)}$ and $\bf{9}$ .
$\frac{(-3) + 9}{2} = \frac{6}{2} = \bf{3}$

So, the x-coordinate of our vertex is $\bf{3}$ !

The axis of symmetry is a vertical line, and its equation always looks like $x = \text{something}$ .

We just found that the x-coordinate of the vertex is $\bf{3}$ .
This means the equation of our axis of symmetry is $x = 3$ .
Boom!

The equation of the axis of symmetry is $x = 3$ .