Math / Algebra

Question7. Find the axis of symmetry of the graph of $g(x)=x^{2}-5 x+2$ . A. $0 x=-5$ B. $x=2$ C. $\quad x=\frac{5}{2}$ D. $x=-\frac{5}{2}$

Studdy Solution

STEP 1

What is this asking? Find the x-value of the vertex of a parabola. Watch out! Don't mix up the formula for the axis of symmetry with other quadratic formulas!

STEP 2

1. Find the values of a, b, and c.
2. Use the axis of symmetry formula.

STEP 3

Alright, let's kick things off by looking at our quadratic function, which is in the standard form: $g(x) = ax^2 + bx + c$ .
We need to identify our a, b, and c values!

STEP 4

In our case, $g(x) = x^2 - 5x + 2$ .
This means our a is 1 (since $x^2$ is the same as $1 \cdot x^2$ ), our b is -5, and our c is a nice and positive 2.
Excellent!

STEP 5

Now, for the main event: the axis of symmetry formula!
It's a super handy formula: $x = -\frac{b}{2a}$ .
This formula tells us the x-value of the vertex of a parabola, which is exactly what we're looking for!

STEP 6

Let's plug in our a and b values.
Remember, we found that a = 1 and b = -5.
So, we have $x = -\frac{-5}{2 \cdot 1}$ .

STEP 7

A negative times a negative makes a positive, so our numerator becomes 5.
And $2 \cdot 1$ is just 2.
So, we have $x = \frac{5}{2}$ .
Boom!

STEP 8

The axis of symmetry is $x = \frac{5}{2}$ , which means the correct answer is C!

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Question7. Find the axis of symmetry of the graph of $g(x)=x^{2}-5 x+2$ . A. $0 x=-5$ B. $x=2$ C. $\quad x=\frac{5}{2}$ D. $x=-\frac{5}{2}$

Studdy Solution

STEP 1

What is this asking? Find the x-value of the vertex of a parabola. Watch out! Don't mix up the formula for the axis of symmetry with other quadratic formulas!

STEP 2

1. Find the values of a, b, and c.
2. Use the axis of symmetry formula.

STEP 3

Alright, let's kick things off by looking at our quadratic function, which is in the standard form: $g(x) = ax^2 + bx + c$ .
We need to identify our a, b, and c values!

STEP 4

In our case, $g(x) = x^2 - 5x + 2$ .
This means our a is 1 (since $x^2$ is the same as $1 \cdot x^2$ ), our b is -5, and our c is a nice and positive 2.
Excellent!

STEP 5

Now, for the main event: the axis of symmetry formula!
It's a super handy formula: $x = -\frac{b}{2a}$ .
This formula tells us the x-value of the vertex of a parabola, which is exactly what we're looking for!

STEP 6

Let's plug in our a and b values.
Remember, we found that a = 1 and b = -5.
So, we have $x = -\frac{-5}{2 \cdot 1}$ .

STEP 7

A negative times a negative makes a positive, so our numerator becomes 5.
And $2 \cdot 1$ is just 2.
So, we have $x = \frac{5}{2}$ .
Boom!

STEP 8

The axis of symmetry is $x = \frac{5}{2}$ , which means the correct answer is C!

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Question7. Find the axis of symmetry of the graph of g(x)=x2−5x+2g(x)=x^{2}-5 x+2g(x)=x2−5x+2. A. 0x=−50 x=-50x=−5 B. x=2x=2x=2 C. x=52\quad x=\frac{5}{2}x=25​ D. x=−52x=-\frac{5}{2}x=−25​

Studdy Solution

STEP 1

What is this asking? Find the *x*-value of the vertex of a parabola. Watch out! Don't mix up the formula for the axis of symmetry with other quadratic formulas!

STEP 2

1. Find the values of *a*, *b*, and *c*.2. Use the axis of symmetry formula.

STEP 3

Alright, let's **kick things off** by looking at our quadratic function, which is in the **standard form**: g(x)=ax2+bx+cg(x) = ax^2 + bx + cg(x)=ax2+bx+c.We need to **identify** our *a*, *b*, and *c* values!

STEP 4

In our case, g(x)=x2−5x+2g(x) = x^2 - 5x + 2g(x)=x2−5x+2.This means our *a* is **1** (since x2x^2x2 is the same as 1⋅x21 \cdot x^21⋅x2), our *b* is **-5**, and our *c* is a nice and positive **2**.Excellent!

STEP 5

Now, for the **main event**: the axis of symmetry formula!It's a **super handy** formula: x=−b2ax = -\frac{b}{2a}x=−2ab​.This formula tells us the *x*-value of the vertex of a parabola, which is exactly what we're looking for!

STEP 6

Let's **plug in** our *a* and *b* values.Remember, we found that *a* = **1** and *b* = **-5**.So, we have x=−−52⋅1x = -\frac{-5}{2 \cdot 1}x=−2⋅1−5​.

STEP 7

A negative times a negative makes a positive, so our numerator becomes **5**.And 2⋅12 \cdot 12⋅1 is just **2**.So, we have x=52x = \frac{5}{2}x=25​.Boom!

STEP 8

The axis of symmetry is x=52x = \frac{5}{2}x=25​, which means the correct answer is C!

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Question7. Find the axis of symmetry of the graph of $g(x)=x^{2}-5 x+2$ . A. $0 x=-5$ B. $x=2$ C. $\quad x=\frac{5}{2}$ D. $x=-\frac{5}{2}$

What is this asking? Find the x-value of the vertex of a parabola. Watch out! Don't mix up the formula for the axis of symmetry with other quadratic formulas!

1. Find the values of a, b, and c.
2. Use the axis of symmetry formula.

Alright, let's kick things off by looking at our quadratic function, which is in the standard form: $g(x) = ax^2 + bx + c$ .
We need to identify our a, b, and c values!

In our case, $g(x) = x^2 - 5x + 2$ .
This means our a is 1 (since $x^2$ is the same as $1 \cdot x^2$ ), our b is -5, and our c is a nice and positive 2.
Excellent!

Now, for the main event: the axis of symmetry formula!
It's a super handy formula: $x = -\frac{b}{2a}$ .
This formula tells us the x-value of the vertex of a parabola, which is exactly what we're looking for!

Let's plug in our a and b values.
Remember, we found that a = 1 and b = -5.
So, we have $x = -\frac{-5}{2 \cdot 1}$ .

A negative times a negative makes a positive, so our numerator becomes 5.
And $2 \cdot 1$ is just 2.
So, we have $x = \frac{5}{2}$ .
Boom!

The axis of symmetry is $x = \frac{5}{2}$ , which means the correct answer is C!