Write each quadratic equation in factored form and standard form. State which way the parabola opens.
Zeros= -1 and -7
Points on the graph= (3, 5)
To find the quadratic equation in factored form, we can start by using the zeros -1 and -7. The factored form of a quadratic equation with zeros x1 and x2 is given by (x - x1)(x - x2).
In this case, the factored form is (x - (-1))(x - (-7)), which simplifies to (x + 1)(x + 7).
To write the equation in standard form, we need to expand the factored form. Multiplying (x + 1)(x + 7), we get x^2 + 7x + x + 7, which simplifies to x^2 + 8x + 7.
Therefore, the quadratic equation in factored form is (x + 1)(x + 7), and the equation in standard form is x^2 + 8x + 7.
To determine which way the parabola opens, we can look at the coefficient of the x^2 term. In this case, the coefficient is positive (1), so the parabola opens upward.