Help me please
Standard form:
y=x^2-2x-3
Vertex form:
???
Intercept form:
???
Y = x^2 - 2x - 3
Vertex Form: Y = a(x-h)^2 + k
h = -b/2a = 2/2 = 1
K = 1^2 - 2*1 - 3 = -4
Vertex Form: Y = 1(x-1)^2 - 4
Y = x^2 - 2x - 3 = 0
-3 = 1*(-3). Sum = 1 + (-3) = -2 = b.
Factored or Intercept form:(x+1)(x-3) = 0
Of course, I'm here to help! Let's go through each form one by one and I'll explain how to convert the given quadratic equation into each form.
1. Standard Form:
The standard form of a quadratic equation is given by: y = ax^2 + bx + c.
For the given equation y = x^2 - 2x - 3, it is already in the standard form.
2. Vertex Form:
The vertex form of a quadratic equation is given by: y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
To rewrite the equation in vertex form, we need to complete the square. Follow these steps:
- Start with the equation in standard form: y = x^2 - 2x - 3.
- Complete the square for the x terms by adding and subtracting the square of half the coefficient of x. In this case, the coefficient of x is -2, so we need to add and subtract (-2/2)^2 = 1.
y = x^2 - 2x + 1 - 1 - 3
- Rearrange the equation by grouping the x terms and the constant term:
y = (x^2 - 2x + 1) - 4
- Simplify the equation by factoring the perfect square expression and combining like terms:
y = (x - 1)^2 - 4
- Now, the equation is in vertex form with the vertex at (1, -4).
3. Intercept Form:
The intercept form of a quadratic equation is given by: y = a(x - p)(x - q), where p and q represent the x-intercepts (also known as roots or zeros) of the equation.
To rewrite the equation in intercept form, we need to find the x-intercepts. Follow these steps:
- Set y = 0 and solve for x to find the x-intercepts:
0 = x^2 - 2x - 3
This equation can be factored as (x - 3)(x + 1) = 0
- Therefore, the x-intercepts are x = 3 and x = -1.
- Substitute these values into the intercept form equation: y = a(x - 3)(x + 1)
Now you have the equation in standard, vertex, and intercept form. Feel free to ask any more questions if needed!