Consider the quadratic function below and (a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or a minimum value, and find that value; and (d) graph the function. \[ f(x)=x^{2}-14 x+48 \] (a) The vertex occurs at \( \square \). (Type an ordered pair, using integers or fractions.)
Added by Brandon G.
Close
Step 1
The vertex of a quadratic function in the form \(f(x) = ax^2 + bx + c\) can be found using the formula \(x = -\frac{b}{2a}\). For the given function \(f(x) = x^2 - 14x + 48\), we have \(a = 1\) and \(b = -14\). - Calculate the x-coordinate of the vertex: \[x = Show more…
Show all steps
Your feedback will help us improve your experience
Pritesh Ranjan and 81 other Algebra educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
a) Find the vertex. b) Find the axis of symmetry. c) Determine whether there is a maximum or minimum value and find that value. d) Graph the function. $$f(x)=-3 x^{2}+4 x+4$$
Systems of Equations and Matrices
Matrix Operations
(a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value, and find that value; and (d) graph the function. $$f(x)=x^{2}-8 x+12$$
Quadratic Functions and Equations; Inequalities
Analyzing Graphs of Quadratic Functions
(a) find the vertex; (b) find the axis of symmetry; (c) determine whether there is a maximum or minimum value, and find that value; and (d) graph the function $$f(x)=2 x^{2}-10 x+14$$
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD