How to get from general form to intercept form in quadratic equations. I'm not sure if it's possible. Or how do you get from vertex form to intercept form. .?.
To convert a quadratic equation from general form to intercept form, or from vertex form to intercept form, it is indeed possible and can be done by following specific steps. Let's go through each conversion process:
1. General Form to Intercept Form:
The general form of a quadratic equation is usually written as:
ax² + bx + c = 0, where a, b, and c are constants.
To convert this equation to intercept form, also known as factored form, where we can easily determine the x-intercepts (zeros) of the equation, follow these steps:
Step 1: Factor the quadratic equation.
- If the equation can be factored, then set it equal to zero by subtracting the constant term from both sides.
Step 2: Write the equation in intercept form.
- Once factored, the equation will have the form:
a(x - r₁)(x - r₂) = 0, where r₁ and r₂ are the roots or x-intercepts of the equation.
And that's it! You have successfully converted the quadratic equation from general form to intercept form.
2. Vertex Form to Intercept Form:
The vertex form of a quadratic equation is usually written as:
y = a(x - h)² + k, where a, h, and k are constants representing the vertex coordinates (h, k).
To convert this equation to intercept form, we need to expand and simplify the equation. Follow these steps:
Step 1: Expand and simplify the vertex form equation.
- Expand the equation using the distributive property of multiplication, then simplify.
Step 2: Set the expanded equation equal to zero.
- By moving all terms to one side, set the equation equal to zero.
Step 3: Factor (if possible).
- If the equation can be factored, factor it.
Step 4: Write the equation in intercept form.
- Once factored, the equation will have the form:
a(x - r₁)(x - r₂) = 0, where r₁ and r₂ are the x-intercepts.
By following these steps, you will transform a quadratic equation from vertex form to intercept form.
Remember, both conversions involve factoring the quadratic equation to determine its x-intercepts, but the starting form differs.