Questions: Fill in the info below, and graph on your own paper. Then graph the parabola on the axes below by first clicking on the vertex, and then on another point close to the vertex that fits on the axes. You may not be able to click on an x or y intercept. y = -x^2 + 8x - 15 1. State whether the parabola opens up or down? O Up O Down 2. State the vertex as an ordered pair: 3. State the y-intercept as an ordered pair: 4. Write the Equation of the Axis of Symmetry: 5. Click on the vertex and then another point of the parabola that fits on the axes below.

Fill in the info below, and graph on your own paper. Then graph the parabola on the axes below by first clicking on the vertex, and then on another point close to the vertex that fits on the axes. You may not be able to click on an x or y intercept. y = -x^2 + 8x - 15 1. State whether the parabola opens up or down? O Up O Down 2. State the vertex as an ordered pair: 3. State the y-intercept as an ordered pair: 4. Write the Equation of the Axis of Symmetry: 5. Click on the vertex and then another point of the parabola that fits on the axes below.
Transcript text: Fill in the info below, and graph on your own paper. Then graph the parabola on the axes below by first clicking on the vertex, and then on another point close to the vertex that fits on the axes. You may not be able to click on an $x$ or $y$ intercept. \[ y=-x^{2}+8 x-15 \] 1. State whether the parabola opens up or down? O UpO Down 2. State the vertex as an ordered pair: $\square$ 3. State the $y$-intercept as an ordered pair: $\square$ 4. Write the Equation of the Axis of Symmetry: $\square$ 5. Click on the vertex and then another point of the parabola that fits on the axes below.
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Solution

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Solution Steps

Step 1: Determine the direction of the parabola

The equation is in the form $y = ax^2 + bx + c$. Here, $a = -1$, $b = 8$, and $c = -15$. Since $a < 0$, the parabola opens downwards.

Step 2: Calculate the vertex

The x-coordinate of the vertex is given by $x = -\frac{b}{2a}$. Substituting $b=8$ and $a=-1$, we have $x = -\frac{8}{2(-1)} = 4$.

Now, substitute $x=4$ back into the equation to find the y-coordinate: $y = -(4)^2 + 8(4) - 15 = -16 + 32 - 15 = 1$. So, the vertex is $(4, 1)$.

Step 3: Calculate the y-intercept

The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation: $y = -(0)^2 + 8(0) - 15 = -15$. Thus, the y-intercept is $(0, -15)$.

Final Answer:

  1. Down
  2. (4, 1)
  3. (0, -15)
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