Express the quadratic function h(x)=(x-r)(x-s) in standard form, and identify a,b, and c.

Question

Question

math algebra

Answer 1

Answer #1

Given that h(x) = (x-r)(x-s)

i.e., h(x) = x²-(r+s)x+r*s

This is the standard form.

Comparing with h(x) = ax²+bx+c we get,

a = 1, b = -(r+s), c = r*s.

Answer 2

Similar Homework Help Questions

■In Problems il-20, express the quadratic function in stan- dard form, and identify a, b, and...

■In Problems il-20, express the quadratic function in stan- dard form, and identify a, b, and e. In Problems 21-22, write an expression (x) for the result of the given operations on x, and put it in standard form 1. Add 5, multiply by x, subtract 2 22 Subtract 3, multiply by x, add 2, multiply by 5 25. If a company charges x dollars per item, it finds that it can sell 1500-3x of them. Each item costs $5...
A quadratic function fis given. F(x) = 1 - 4x - x² (a) Express fin standard...

A quadratic function fis given. F(x) = 1 - 4x - x² (a) Express fin standard form. f(x) - 1 - x(x +4) X (b) Sketch a graph of f. у
6. Write the quadratic function f(x-ar' + br + c , a * 0 İn vertex form f(x) = a(x-h)' + k using ...

6. Write the quadratic function f(x-ar' + br + c , a * 0 İn vertex form f(x) = a(x-h)' + k using e fo rmulas for h and k in terms of the procedure of completing the perfect square and provid parameters a, b, and c. Solve the equ formula. Factor the quadratic expression ax+br+c in terms of the solutions x, and x, of the quadratic equation. Write equations expressing the relationships between parameter a, b and c and...

17) Given the quadratic function g(x)= -x2 - 4x + 4 a) Express the quadratic function...

17) Given the quadratic function g(x)= -x2 - 4x + 4 a) Express the quadratic function in standard forn b) Find its vertex.
Consider the following nonlinear program: min s.t. - (a) Express the objective function of the above problem in the standard quadratic function form: (b) Find the gradient and the Hessian of...

Consider the following nonlinear program: min s.t. - (a) Express the objective function of the above problem in the standard quadratic function form: (b) Find the gradient and the Hessian of f(x). (c) If possible, solve the minimisation problem and give reasons why the solution you found is a global minimum rather than just a local minimum. Otherwise, demonstrate that the problem is unbounded. f (x: y) = (x + 2y)2-2x-y We were unable to transcribe this imageWe were unable...
also, identify the vertex. no need to sketch. Write the quadratic function in a(x-h)^2+k form (Hint:...

also, identify the vertex. no need to sketch. Write the quadratic function in a(x-h)^2+k form (Hint: Find the vertex first to determine h and k). f(x) = x2 - 4x + 7 f(x) = Sketch its graph. 20 Graph Layers 18 16 14 After you add a can use Graph properties 12 -10 Fill 8 8 2 2013-10-14 12 10 8 -8 42 2 4 8 8 10 12 14 18 19 20 -2 2 No Solution -B -B -10...

The following equation of a quadratic function is given in standard form. f(x) = 2x² -...

The following equation of a quadratic function is given in standard form. f(x) = 2x² - 12x + 21 Find the same equation in vertex form, then enter it below. Round your answers to the nearest tenth if necessary. f(x) = (x - )? +
Write the quadratic function in the form f (x)= a (x- h)ʻ+k. Then, give the vertex...

Write the quadratic function in the form f (x)= a (x- h)ʻ+k. Then, give the vertex of its graph. f(x)=-3x² +18x-31 Writing in the form specified: f(x) = I Vertex:
Write the quadratic function in the form f(x)=a(x-h)^2+k; Find the vertex and graph the function (a) f(x)=x^2-6x (b) f(x)=-x^2+4x+1 (c) f(x)=3x^2-10x+2

Write the quadratic function in the form f(x)=a(x-h)^2+k; Find the vertex and graph the function (a) f(x)=x^2-6x (b) f(x)=-x^2+4x+1 (c) f(x)=3x^2-10x+2

Let A be n × n with AT-A. (The matrix A is syrnmetric.) Let B be 1 × n and let c E R. Define f : Rn → R by f(x) = 2.7, A . x + B . x + c. Show that The function f is a quadratic function Let...

Let A be n × n with AT-A. (The matrix A is syrnmetric.) Let B be 1 × n and let c E R. Define f : Rn → R by f(x) = 2.7, A . x + B . x + c. Show that The function f is a quadratic function Let A be n × n with AT-A. (The matrix A is syrnmetric.) Let B be 1 × n and let c E R. Define f : Rn...