9. Show that the graph of the quadratic equation in one variable Ax² + Dx + F = 0 is one line, two parallel lines, or that no real value of x satis- fies the equation, according as the discriminant D²-4AF is zero, positive, or negative.

Q: What is the vertex of the following quadratic equation? y = x +8x O (-4, 16) O (4, -16) O (4, 16) O…

A: It can be expressed as the general form of parabola.

Q: i have a question about the step by step of 0= -x2+4x-5 using the quadratic formula

A: Consider the quadratic equation, -x2+4x-5=0 To solve the given equation,…

Q: 1. Consider the quadratic equation 3x -6 = 2x. (a) What is the value of the discriminant? (b) What…

A:

Q: Write a quadratic equation in X such that the sum of itr roots is -2 and the product of its roots is…

A:

Q: I was asked to write an equation of the quadratic with the following features: x-intercepts (-3,0)…

A: Given that (–3,0) and (1,0) are x-intercepts. This implies that –3 and 1 are zeros of the function y…

Q: Suppose f (x) = x² + 2x + 1. Find the vertex, vertical intercept, and x-intercepts of this quadratic…

A: The objective of the question is evaluate vertex , vertical intercept and  x-intercept.

Q: when finding the x-intercept of 0=(x+4)2 -9, is it plus and minus on both sides?

A: Given Equation is as follows

Q: or a certain company, the monthly profits earned by investing x dollars per month in publication are…

A: Given profit function is,  U=−0.12x2+510x−25000

Q: r(x) is the image of y=2x2+12x+2 after a translation left 2 units and up 3 units, write the equation…

A:

Q: raph the quadratic function given in standard form

A: given vertex given ( -2 , -1 )

Q: Determine whether the equation x² + 1 = 0 has a solution in F3.

A:

Q: 22. Suppose a quadratic equation has the form x² + x + c = 0. Show that the constant c must be less…

A:

Q: The population of a certain country was approximately 75 million in 1900, 175 million in 1950, and…

A: We have to find quadratic equation and population in 2050

Q: 1) Solve the following equation written in the form = G(ax +by). = (2x + y)² + 6(2x + y) + 7

A:

Q: Find an equation for the given line in the form ax + by = c, where a, b, and are integers with no…

A: Slope of any two parallel line is same.

Q: The population of a certain country was approximately 50 million in 1900, 150 million in 1950, and…

A: Given that the data The population of a certain country was approximately 50 million in 1900, 150…

Q: If the discriminant of a quadratic equation is 0, then the equation has

A:

Q: Find the equation of the line that is perpendicular to 2x+3y=4 and goes through the point (2,3). If…

A:

Q: Solve (x + 2)x 4 geometrically by constructing a line segment of length x .

A: We can expand it by multiplying x inside bracket then it is parabola equation then draw the parabola…

Q: 6. Show that the quadratic equation ax² + b – a = 0 (a± 0) has two distinct real roots.

A: