The Vertex of the Parabola: Finding a stationary point

To answer the question, we must first remember the formula for finding the vertex of a parabola:

Now let's substitute the known data into the formula:

-5/2(-1)=-5/-2=2.5

In other words, the x-coordinate of the vertex of the parabola is found when the X value equals 2.5.

Now let's substitute this into the parabola equation to find the Y value:

-(2.5)²+5*2.5+6= 12.25

Therefore, the coordinates of the vertex of the parabola are (2.5, 12.25).

To calculate point B, we should determine the vertex of the quadratic function $f(x) = x^2 - 6x + 8$.

The x-coordinate of the vertex can be found using the formula $x = -\frac{b}{2a}$.

In our equation, we have $a = 1$ and $b = -6$, therefore:

$x = -\frac{-6}{2 \times 1} = \frac{6}{2} = 3$

Next, we substitute $x = 3$ back into the function to find the y-coordinate:

$f(3) = 3^2 - 6 \times 3 + 8 = 9 - 18 + 8 = -1$

Thus, the vertex, which is point B, is $(3, -1)$.

Therefore, the solution indicates that point B is at $(3, -1)$.

To solve the exercise, first note that point C lies on the X-axis.

Therefore, to find it, we need to understand what is the X value when Y equals 0.

Let's set the equation equal to 0:

0=x²-8x+16

We'll use the preferred method (trinomial or quadratic formula) to find the X values, and we'll discover that

X=4

To solve this problem, we'll calculate the vertex of the parabola given by the quadratic function $f(x) = x^2 - 6x$.

• Step 1: Identify the coefficients $a = 1$ and $b = -6$.
• Step 2: Use the vertex formula $x = -\frac{b}{2a}$ to find the x-coordinate of the vertex.
• Step 3: Substitute the calculated x-coordinate back into the function to find the y-coordinate.

Now, let's compute:

Step 1: The function is $f(x) = x^2 - 6x$ with coefficients $a = 1$ and $b = -6$.

Step 2: Apply the vertex formula: $x = -\frac{-6}{2 \times 1} = \frac{6}{2} = 3$.

Step 3: For $x = 3$, substitute into $f(x)$ to find the y-coordinate:

$f(3) = (3)^2 - 6 \times 3 = 9 - 18 = -9$.

Therefore, the coordinates of the point C, which is the vertex, are $(3, -9)$.

The correct answer is $(3, -9)$, which corresponds to the given correct choice.