Symmetry: Axis of symmetry

To solve this problem, we'll follow these steps:

• Step 1: Identify the coefficients in the quadratic equation.
• Step 2: Apply the formula for the axis of symmetry.
• Step 3: Substitute the coefficients into the formula and solve.

Now, let's work through each step:
Step 1: The quadratic function given is $f(x) = 7x^2$ which can be written in the form $ax^2 + bx + c$. Here, $a = 7$, $b = 0$, and $c = 0$.
Step 2: We'll use the formula for the axis of symmetry: $x = -\frac{b}{2a}$.
Step 3: Substitute $a = 7$ and $b = 0$ in the formula:
$x = -\frac{0}{2 \times 7} = 0$ Therefore, the axis of symmetry for the quadratic function $f(x) = 7x^2$ is $x = 0$.

Therefore, the solution to the problem is $x = 0$, corresponding to choice #3.

To find the axis of symmetry for the quadratic function $f(x) = 4x^2 + 6$, we employ the formula for the axis of symmetry of a parabola given by $ax^2 + bx + c$, which is $x = -\frac{b}{2a}$.

Given $f(x) = 4x^2 + 0x + 6$, we identify the coefficients from the function:

• $a = 4$
• $b = 0$

Substituting these values into the formula:

$x = -\frac{b}{2a} = -\frac{0}{2 \times 4} = 0$

Thus, the axis of symmetry for the quadratic function is $x = 0$.

Therefore, the solution to the problem is $\mathbf{x = 0}$.

To determine the axis of symmetry for the function $f(x) = 3x^2 + 2$, we follow these steps:

• Identify the coefficients from the function. Here, $a = 3$ and $b = 0$. The constant term $c = 2$ does not affect the axis of symmetry.
• Use the axis of symmetry formula for a quadratic function: $x = -\frac{b}{2a}$.
• Substitute the values for $b$ and $a$ into the formula: $x = -\frac{0}{2 \times 3} = 0$.

This calculation shows that the axis of symmetry for the graph of the quadratic function is $x = 0$.

Thus, the solution to the problem is that the axis of symmetry is $x = 0$.

To solve this problem, we'll apply the formula for the axis of symmetry of a quadratic function:

• Step 1: Recognize the function is $f(x) = 2x^2 + 8x + 4$.
• Step 2: Identify the coefficients: $a = 2$ and $b = 8$.
• Step 3: Use the axis of symmetry formula $x = -\frac{b}{2a}$.

Now, substituting the values of $a$ and $b$ into the formula:
$x = -\frac{8}{2 \times 2}$,
$x = -\frac{8}{4}$,
$x = -2$.

Therefore, the axis of symmetry for the given quadratic function is $x = -2$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the coefficients $a$ and $b$.
• Step 2: Apply the symmetry axis formula.
• Step 3: Simplify the expression to find the solution.

Now, let's work through each step:

Step 1: From the quadratic function $f(x) = -2x^2 + 16$, we identify the coefficients: $a = -2$ and $b = 0$.

Step 2: Using the formula for the axis of symmetry, $x = -\frac{b}{2a}$, we substitute the identified coefficients:

$x = -\frac{0}{2(-2)}$.

Step 3: Simplifying the expression, we have:

$x = 0$.

Therefore, the solution to the problem is the axis of symmetry: $x = 0$.

To find the axis of symmetry for the quadratic function $f(x) = 3x^2 + 6x - 6$, we begin by identifying the coefficients in the general form of a quadratic equation: $ax^2 + bx + c$. Here, $a = 3$, $b = 6$, and $c = -6$.

The formula for the axis of symmetry of a quadratic function is:

$x = -\frac{b}{2a}$.

Substituting the given values into the formula, we have:

$x = -\frac{6}{2 \cdot 3}$.

Calculating the above expression, we get:

$x = -\frac{6}{6} = -1$.

Thus, the axis of symmetry for this quadratic function is $x = -1$.

Therefore, the solution to the problem is $x = -1$.

To solve this problem, we'll determine the axis of symmetry using the appropriate formula:

• Step 1: Identify the coefficients $a$, $b$, and $c$
• Step 2: Use the axis of symmetry formula
• Step 3: Substitute the values and solve

Now, let's work through each step:

Step 1: The quadratic function is $f(x) = x^2 + 4x$. Here, $a = 1$, $b = 4$, and $c = 0$.

Step 2: Use the axis of symmetry formula $x = -\frac{b}{2a}$.

Step 3: Substitute the values: $x = -\frac{4}{2 \times 1} = -\frac{4}{2} = -2$

Therefore, the axis of symmetry for the graph is $x = -2$.

To solve this problem, we'll apply the formula for finding the axis of symmetry for a quadratic function:

• Step 1: Identify the coefficients.
  For the quadratic function $f(x) = x^2 + 4x + 1$, we have $a = 1$ and $b = 4$.
• Step 2: Use the formula for the axis of symmetry.
  The axis of symmetry for a quadratic function $ax^2 + bx + c$ is given by $x = -\frac{b}{2a}$.
• Step 3: Substitute the values of $a$ and $b$ into the formula.
  Substitute $b = 4$ and $a = 1$ to get: $x = -\frac{4}{2 \times 1}$.
• Step 4: Simplify to find the value of $x$.
  This simplifies to $x = -\frac{4}{2} = -2$.

Therefore, the axis of symmetry for the given quadratic function is $x = -2$.

To solve this problem, we'll follow these steps:

• Step 1: Identify the given coefficients $a$ and $b$.
• Step 2: Apply the formula for the axis of symmetry.
• Step 3: Perform the necessary calculations to find the axis of symmetry.

Now, let's work through each step:
Step 1: The given quadratic function is $f(x) = -5x^2 - 25x$, so $a = -5$ and $b = -25$.
Step 2: We'll use the axis of symmetry formula $x = -\frac{b}{2a}$.
Step 3: Plugging in our values, we get $x = -\frac{-25}{2 \times -5} = -\frac{25}{-10} = -2.5$.

Therefore, the axis of symmetry for the quadratic $f(x) = -5x^2 - 25x$ is $x = -2\frac{1}{2}$.

The first step in solving the equation you presented:

y=(x-5)²+15

is to expand the parentheses:

y=x²-10x+25+15

y=x²-10x+40

From here, we can use the formula to find the X-coordinate of the vertex:

-b/2a

Let's substitute the values from the equation:

-(-10)/2*1 =

10/2=5

The axis of symmetry of the parabola is X=5