The vertex of a quadratic function is (2, -4) and the leading coefficient is -2.

Question

The vertex of a quadratic function is (2, -4) and the leading coefficient is -2. What is the vertex form of the equation for this function? For each of the two quadratic functions below, explain how the vertex of the parent function graph would be changed to make the graph of the given function. A. y_1 = x^2 + 4 B. y_2 = (x + 2)^2 - 4 What is the equation for the axis of symmetry to the function y = 3x^2 - 10x + 4 Give the coordinates of the vertex of the graph of the following function. f(x) = x^2 + 4x + 5

Explanation / Answer

2. given:- vertex = (2,-4) and a = -2

As we know that

Vertex Form: y = a(x - h)2 + k

y = -2{ x- 2}2 + (-4)

3.The simplest parabola is

y = x2,

This graph passes through the origin (0,0), and is contained in Quadrants I and II. This graph is known as the "Parent Function" for parabolas, or quadratic functions. All other parabolas, or quadratic functions, can be obtained from this graph by one or more transformations. Let's see then

The first equation given here is

y1 = x2 + 4

This could be obtained by adding 4 in the parent equation

y = x2

y = a(x - h)2 + k

first the vertex of parent equation were h=0 and k=0 and coefficient =1

then the vertex of parent equation were changed to h=0 and k=4 and coefficient =1

In the 2nd equation

the vertex of parent equation were changed to h=-2 and k=-2 and coefficient =1

4. Since this equation is in standard form we use the formula for standard form equation

x=b /2a

f(x) = x2+4x+5

so b = 4 and a = 1

So, the axis of symmetry is the line x=b /2a = -4/2 = -2

x = -2

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.