What the exam asks
| Typical stem | What you actually do |
|---|---|
| What is the minimum (or maximum) value of ? | Find the vertex’s -coordinate |
| Which equivalent form displays the minimum value as a constant or coefficient? | Choose vertex form, |
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Lesson 4 of 6 · Advanced math
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Quadratic functions are the SAT’s favorite nonlinear model. The test asks you to read a parabola’s vertex, intercepts and axis of symmetry from an equation or a graph, to choose the form that displays a feature, to interpret maximums and minimums in context (heights, revenue, area), and, on hard items, to find unknown constants from graph features. Everything rests on one skill: knowing what each form of the equation shows.
| Typical stem | What you actually do |
|---|---|
| What is the minimum (or maximum) value of ? | Find the vertex’s -coordinate |
| Which equivalent form displays the minimum value as a constant or coefficient? | Choose vertex form, |
3 questions on quadratic functions and parabolas. Every option is explained once you answer.
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Vertex form and what it displays
| Which equivalent form displays the -intercepts? | Choose factored form, |
| The graph of is shown. Which equation could define ? | Match the direction, vertex, intercepts and -intercept |
| What is the best interpretation of 3000 in this context? | Translate the vertex (or an intercept) into words |
| The graph passes through... What is the value of (or , , )? | Plug features into the right form and solve |
| Form | Equation | Displays directly | Vertex |
|---|---|---|---|
| Standard | -intercept | , then substitute | |
| Vertex | Vertex , max or min value , axis | ||
| Factored | -intercepts and |
In every form, controls direction and width. If the parabola opens up and the vertex is a minimum. If it opens down and the vertex is a maximum. A larger gives a narrower parabola.
A parabola is symmetric about its axis . So:
| Feature | Typical meaning |
|---|---|
| Vertex -value, | When or at what input the maximum or minimum happens (time of peak height, best price, best width) |
| Vertex -value, | The maximum or minimum itself (peak height, largest revenue or area) |
| -intercept, | The starting value, such as the initial height at |
| Positive -intercept | When the output reaches 0, such as when the object lands |
For projectiles in feet, . In meters, the leading coefficient is . For revenue, : find the zeros, average them, and substitute.
Pick the form that matches what you’re given. For a vertex plus a point, use and substitute the point to get . For zeros plus a point, use . For a vertex location with standard form, use . Never assume .
| Read it off |
| , then substitute |