Questions: Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation for the parabola's axis of symmetry. Use the parabola to identify the function's domain and range. f(x)=(x-1)^2+6 Use the graphing tool to graph the equation. Use the vertex and the y-intercept when drawing the graph. Click to enlarge graph The axis of symmetry is (Simplify your answer. Type in equation.) Identify the function's domain. The domain is . (Type the answer in interval notation.) Identify the function's range. The range is (Type the answer in interval notation.)

Use the vertex and intercepts to sketch the graph of the quadratic function. Give the equation for the parabola's axis of symmetry. Use the parabola to identify the function's domain and range. f(x)=(x-1)^2+6 Use the graphing tool to graph the equation. Use the vertex and the y-intercept when drawing the graph. Click to enlarge graph The axis of symmetry is (Simplify your answer. Type in equation.) Identify the function's domain. The domain is . (Type the answer in interval notation.) Identify the function's range. The range is (Type the answer in interval notation.)

Solution

failed
failed

Solution Steps

Step 1: Domain and Range

The domain of the quadratic function is always \((-\infty, \infty)\). Given that the coefficient \(a = 1\), the range of the function is \([6, \infty)\).

Step 2: Vertex

The vertex of the parabola is directly given by the parameters \(h\) and \(k\) as the point \((1, 6)\).

Step 3: Axis of Symmetry

The axis of symmetry can be found using the formula \(x = 1\).

Step 4: Y-intercept

To find the y-intercept, set \(x = 0\) in the function to get \(f(0) = 7\).

Step 5: X-intercepts

To find the x-intercepts, solve for \(x\) when \(f(x) = 0\). The x-intercepts are: No real x-intercepts.

Final Answer:

Domain: \((-\infty, \infty)\), Range: \([6, \infty)\), Vertex: \((1, 6)\), Axis of Symmetry: \(x = 1\), Y-intercept: 7, X-intercepts: No real x-intercepts

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Tissue fluid becomes lymph once it has entered a lymphatic capillary; lymph formation depends on tissue fluid formation. Tissue fluid is made up of Blank 1 and dissolved substances that leave blood capillaries by the process of Blank 2. The Blank 3 pressure of tissue fluid drive the entry of lymph into lymphatic capillaries. A condition that interferes with the flow of lymph will result in a condition called Blank 4. Lymph nodes are Blank 5 shaped with blood vessels, nerves, and efferent lymphatic vessels attached to the indentation, called the Blank 6, and with afferent lymphatic vessels entering on the convex surface. The white blood cells within lymph nodes filter Blank 7, and remove bacteria and cellular debris before it is returned to the blood. Lymph nodes are also centers of Blank 8 production; these cells function in immune surveillance.
failedAnswered
Schwartr Industry is an industrial company with 93.4 million shares outstanding and a market capitalization (equity value) of 4.27 billion. It has 1.17 billion of debt outstanding. Management has decided to delever the firm by issuing new equity to repay all outstanding debt. a. How many new shares must the firm issue? b. Suppose you are a shareholder holding 100 shares, and you disagree with this decision. Assuming a perfect capital market, describe what you can do to undo the effect of this decision. The firm must issue million shares. (Round to one decimal place.)
failedAnswered
In a double-blind study, researchers tested whether small doses of caffeine would improve highly trained male cyclists' times in a hot environment (95 degrees F, 25% humidity). The individuals were 9 highly trained male cyclists who rode a stationary bicycle in a hot climate chamber on three separate occasions. The first session was a familiarization session. On the second session, some athletes took a caffeine pill and the rest took a placebo pill of Metamucil. On the third session, each athlete took the other pill. For each of the second and third sessions, the cyclists were randomly assigned to the treatment and control groups. The study concluded that a small dose of caffeine improves a highly trained male cyclist's time in a hot environment. Complete parts (a) through (d) below. a. Describe the treatment and control groups. Choose the correct answer below. A. The treatment group is the 9 male cyclists after the sessions. The control group is the 9 male cyclists before the sessions. B. The treatment group is the 9 male cyclists before the sessions. The control group is the 9 male cyclists after the sessions. C. The treatment group is the 9 male cyclists when they took Metamucil. The control group is the 9 male cyclists when they took the caffeine pill. D. The treatment group is the 9 male cyclists when they took the caffeine pill. The control group is the 9 male cyclists when they took Metamucil.
failedAnswered
1. El número de calorías que se queman en una hora de ejercicio en una máquina de ejercicios, es una función de la velocidad que se emplea. Si una persona que se ejercita a una velocidad de 2,5 kilómetros por hora, quema 210 calorías y a 6 kilómetros por hora, esta persona quemará 370 calorías. Sea C las calorías quemadas en una hora y V la velocidad de la maquina de ejercicios. a) Determine un modelo lineal que representa en número de calorias quemadas en función de la velocidad. b) Interprete la pendiente y el intercepto. c) ¿Cuántas calorías se queman si la persona se ejercita a una velocidad de 5 kilómetros por hora? d) ¿A qué velocidad ejercita una persona que esta quemando 150 calorías? e) Invierta el modelo y defina según el contexto las variables.
failedAnswered
Multiple Select Question Select all that apply Most fruits are - good sources of potassium and folate. - low in fiber. - good sources of protein. - low in fat. - good sources of phytochemicals.