Let's go through the questions based on the quadratic function provided:

$f(x) = -3x^2 + 9$

1) Identify the coefficients a, b, and c:

The quadratic function is in the form $f(x) = ax^2 + bx + c$, where:

• $a = -3$ (the coefficient of $x^2$),
• $b = 0$ (there is no $x$-term),
• $c = 9$ (the constant term).

2) Graph the function on your calculator:

You can input the function $f(x) = -3x^2 + 9$ into your calculator to plot it. The graph will be a parabola that opens downward (because $a = -3$, which is negative), and it will have its vertex at the maximum point.

3) Does the graph open up or down and why?

The graph opens down because the coefficient of $x^2$ (which is $a$) is negative ($a = -3$).

4) Write the Vertical Intercept as an Ordered Pair:

The vertical intercept occurs when $x = 0$. Substituting $x = 0$ into the function: $f(0) = -3(0)^2 + 9 = 9$ Thus, the vertical intercept is $(0, 9)$.

5) Plot the Vertical Intercept on the graph:

Plot the point $(0, 9)$ on the y-axis.

6) Draw the function neatly on the graph:

The highest point on the graph is the vertex at $(0, 9)$, and since the parabola opens downward, you can plot other points such as:

• For $x = 1$ and $x = -1$, $f(1) = -3(1)^2 + 9 = 6$, so the points $(1, 6)$ and $(-1, 6)$ are on the graph.

You can then draw the parabola based on these points.

Would you like further details or clarification on any of these steps?

Relative Questions:

1. How do you determine the direction of a parabola from its equation?
2. What is the significance of the vertex in the graph of a quadratic function?
3. How can you find the axis of symmetry for a quadratic function?
4. What does the coefficient $a$ tell you about the graph's width?
5. How do you calculate other points on the parabola besides the vertex?

Tip:

The vertex of a parabola in standard form $f(x) = ax^2 + bx + c$ can be found using the formula $x = -\frac{b}{2a}$.