Math Problem Statement

Find the vertex, axis of symmetry, and any
x

  • or
    y -intercepts of
    f ( x ) = x 2

x − 1 . Then graph the function. Give exact answers using fractions and square roots, not decimals. If the function does not have the requested characteristic, enter DNE. If there are multiple instances of a characteristic, separate them with commas.

a) Vertex (as an ordered pair):

b) Equation of the line of symmetry:

c) Range (in interval notation) .

d)
x -intercept(s) (as ordered pair(s)): .

e)
y -intercept (as ordered pair): .

f) Graph:

1 2 3 -1 -2 -3 1 2 3 -1 -2 -3

Solution

Here is the graph of the quadratic function f(x)=x2+x−1f(x) = x^2 + x - 1 with its key features such as the vertex, intercepts, and axis of symmetry clearly shown.

If you have any further questions or need more details, feel free to ask!

Related Questions:

  1. How do you determine whether a parabola opens upwards or downwards?
  2. Can a parabola have more than two x-intercepts?
  3. What happens to the graph if you change the value of the coefficient aa in a quadratic function?
  4. How can we find the vertex if the quadratic function is not in standard form?
  5. What are the steps to graph a quadratic function by hand?

Tip: The vertex form of a quadratic equation can make it easier to graph and find the vertex directly!

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Math Problem Analysis

Mathematical Concepts

Algebra
Quadratic Functions
Graphing
Intercepts

Formulas

Vertex formula: x = -b / 2a for a quadratic function ax^2 + bx + c
Quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a
Standard form of a quadratic equation: f(x) = ax^2 + bx + c

Theorems

Quadratic formula
Symmetry of parabolas
Intercept theorem

Suitable Grade Level

Grades 9-10

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