# Quadratic Equation passing through two points

Find coefficients and x-intercepts of a Quadratic Equation

1. y = 2x² + bx + c

2. passes through points A (0,5) and B(-1,0).

• Find

(i) the value of c

(ii) the value of b

(iii) the x-intercepts

 Aug 29, 2012 Quadratic Equation by: Staff Answer: Part I The standard form of a quadratic function (a parabola) is: y = ax² + bx + c --------------------------------------- y = 2x² + bx + c a = 2 (i) the value of “c”        The quadratic function (a parabola) passes through point A (0,5).            When x = 0, y = 5            To solve for the coefficient “c”, substitute 0 for x and 5 for y in the equation given in the problem statement.                y = 2x² + bx + c                5 = 2*0² + b*0 + c                5 = 0 + 0 + c                5 = c                c = 5 (ii) the value of “b”        The quadratic function also passes through point B (-1,0).            When x = -1, y = 0            To solve for the coefficient “b”, substitute -1 for x, 0 for y, and 5 for c in the quadratic function.                y = 2x² + bx + c                0 = 2*(-1)² + b*(-1) + 5                0 = 2*1 + b*(-1) + 5                0 = 2 - b + 5                0 = 2 + 5 - b                0 = 7 - b                0 + b = 7 - b + b                b = 7 + 0                b = 7 ---------------------------------------------

 Aug 29, 2012 Quadratic Equation by: Staff --------------------------------------------- Part II a = 2 b = 7 c = 5 y = ax² + bx + c y = 2x² + 7x + 5 Check the final equation: If the quadratic function passes through point A (0,5), then y must equal 5 when x = 0 y = 2*0² + 7*0 + 5 y = 0 + 0 + 5 y = 5, OK If the quadratic function passes through point B (-1,0), then y must equal 0 when x = -1 y = 2*(-1)² + 7*(-1) + 5 y = 2*1 - 7*1 + 5 y = 2 - 7 + 5 y = 0, OK --------------------------------------------- (iii) the x-intercepts        The final form of the quadratic function is: y = 2x² + 7x + 5        The quadratic equation is: 2x² + 7x + 5 = 0            the x-intercepts can be determined using the quadratic formula, or by factoring.            Determining the x-intercepts by factoring:                2x² + 7x + 5 = 0                (2x + 5)(x + 1) = 0                (2x + 5) = 0                2x + 5 = 0                2x + 5 - 5 = 0 - 5                2x + 0 = 0 - 5                2x = - 5                2x / 2 = - 5 / 2                x * (2 / 2) = - 5 / 2                x * (1) = - 5 / 2                x = - 5 / 2                the first x-intercept, x₁ = - 5 / 2 ---------------------------------------------

 Aug 29, 2012 Quadratic Equation by: Staff ---------------------------------------------Part III               (2x + 5)(x + 1) = 0               (x + 1) = 0               x + 1 = 0               x + 1 - 1 = 0 - 1               x + 0 = 0 - 1               x = - 1               the second x-intercept, x₂ = - 1 summary of final answers     (i) c = 5     (ii) b = 7     (iii) the x-intercepts ∈ {-5/2, -1}Thanks for writing. Staff www.solving-math-problems.com