Question

How to find x intercepts of a quadratic function in standard form

Answer 1

Sure! Let's consider the quadratic function in standard form: y = ax^2 + bx + c. To find the x-intercepts, we set y equal to zero and solve for x. This results in the equation: 0 = ax^2 + bx + c.

Next, we employ the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)] / (2a), to find the solutions for x. The parameters a, b, and c are coefficients of the quadratic equation. For our specific equation, these coefficients are a=1, b=-3, and c=2.

We initially calculate the discriminant (b^2 - 4ac), a crucial part of the quadratic formula. After calculation, the discriminant value comes out to be 1.

Depending on the value of the discriminant, the type and number of solutions change:
- If the discriminant is positive, there are two distinct real solutions.
- If the discriminant is zero, there is one real root.
- If the discriminant is negative, there are two complex roots.

In our case, the discriminant is positive (1), so our equation will yield two real solutions. Substituting the values of a, b, and the discriminant into the quadratic formula, we calculate the two possibilities for x (we call these root1 and root2).

Upon calculation, the first root (root1) turns out to be 2.0, and the second root (root2) is 1.0.

So, the x-intercepts of the given equation are x=2.0 and x=1.0. These are the points where the graph of the quadratic function intersects the x-axis.

Answer 2

• To find the x intercepts of a quadratic function, means to find those values of x for which y equals zero, graphically, it implies to find the values that pass through the x axis.
• There is a standar formula to apply whenever you have to find those vaues. Consider you have the following quadratic function:
  `y=f(x)=ax^2+bx+c`, where "a" is the coefficient of the quadratic term, "b" is the coefficient of the linear term in your equation, and "c" is the y intercept (the value of y when x equals zero).
• Then the x intercepts can be obtained applying the following formula:
  `(-b(+-)√(b^2-4ac) )/(2a)`.
• Remember that the letters a, b and c are the coefficients in your equation.
• You always obtain two intercepts, because of the (+-) in the formula:
  `x_1=(-b+√(b^2-4ac) )/(2a)` and
  `x_2=(-b-√(b^2-4ac) )/(2a)`.
• If the equation is
  `y=3x^2-4x-2`, then a=3, b= -4 and c= -2.