Quadratic function

It is given a quadratic function y = -4x²+5x+c with unknown coefficient c. Determine the smallest integer c for which the graph of f intersects the x-axis at two different points.

Correct answer:

c =  0

Step-by-step explanation:

$$\begin{gathered} D=b^2-4ac>0 \\ {\displaystyle \frac{b^2}{4a}}>c \\ {\displaystyle \frac{5^2}{4(-4)}}>c \\ -1.5625>c;c\min \\ c=0 \end{gathered}$$

Our quadratic equation calculator calculates it.

Try another example

Related math problems and questions:

• A Cartesian framework
  1. In a Cartesian framework, the functions f and g we know that: the function (f) is defined by f (x) = 2x ^ 2, the function (g) is defined by g (x) = x + 3, the point (O) is the origin of the reference, point (C) is the point of intersection of the graph
• Line
  Straight-line passing through points A [-3; 22] and B [33; -2]. Determine the total number of points of the line in which both coordinates are positive integers.
• Function 3
  Function f(x)=a(x-r)(x-s) the graph of the function has x- intercept at (-4, 0) and (2, 0) and passes through the point (-2,-8). Find constant a, r, s.
• Coordinate
  Determine missing coordinate of the point M [x, 120] of the graph of the function f bv rule: y = 5^x
• Quadratic function
  Write the equation of the quadratic function, which includes points A (-1, 10), B (2, 19), C (1,4)
• Quadratic function 2
  Which of the points belong function f:y= 2x²- 3x + 1 : A(-2, 15) B (3,10) C (1,4)
• 600 pencils
  600 pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done?
• Rectangle
  The perimeter of the rectangle is 22 cm and content area 30 cm². Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers.
• Roots and coefficient
  In the equation 2x ^ 2 + bx-9 = 0 is one root x1 = -3/2. Determine the second root and the coefficient b.
• Points on circle
  In the Cartesian coordinate system with the origin O is a sketched circle k /O; r=2 cm/. Write all the points that lie on a circle k and whose coordinates are integers. Write all the points that lie on the circle I / O; r=5 cm / and whose coordinates are
• Sinus
  Determine the smallest integer p for which the equation 4 sin x = p has no solution.
• Exponential equation
  Determine the value of having y in the expression (3^y): (4^-1)=36. Unknown y is a natural number greater than zero.
• Diofant equation
  In the set of integers (Z) solve the equation: 212x +316y =0 Write result with integer parameter t in Z (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
• Four integers
  Fnd four consecutive integers so that the product of the first two is 70 times smaller than the product of the next two.
• Integer
  Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.
• Five numbers in ratio
  Five integers are in the ratio 1: 2: 3: 4: 5. Their arithmetic mean is 12. Determine the smallest of these numbers.
• Unknown number 7
  Calculate unknown number whose 12th power when divided by the 9th power get a number 27 times greater than the unknown number. Determine the unknown number.