You’ve solved the equation successfully using the Quadratic Formula! You get two true statements, so you know that both solutions work: x = 1 or −5. This means the correct answer is a = 1, b = 3, and c = −6. Putting the terms in order gives the standard form x 2 + 3 x – 6 = 0. You correctly found that 3 x + x 2 = 6 becomes 3 x + x 2 – 6 = 0. Remember that in standard form, the equation is written in the form ax 2 + bx + c = 0. 3 x + x 2 = 6 becomes 3 x + x 2 – 6 = 0, so the standard form is x 2 + 3 x – 6 = 0. This means the correct answer is a = 1, b = 3, and c = −6.Ĭorrect. The c must be on the left side of the equation. You put the terms in the correct order, but the right side must be equal to 0. Substitute 1 for a, -3 for b, and -10 for c in the standard form of quadratic equation.Ĭonfirm that the graph of the equation passes through the given three points.Incorrect. Solving the above system using elimination method, we will get Write the three equations by substituting the given x and y-values into the standard form of a parabola equation, Writing the Equation of a Parabola Given Three Pointsįind the equation of a parabola that passes through the points : So, the selling price of $35 per item gives the maximum profit of $6,250. Use the function to find the x-coordinate and y-coordinate of the vertex. The maximum y-value of the profit function occurs at the vertex of its parabola. The x-axis shows the selling price and the y-axis shows the profit. Once we have three points associated with the quadratic function, we can sketch the parabola based on our knowledge of its general shape. In the vertex (2, 4), the x-coordinate is 2.įind the y-intercept of the quadratic function.įind a point symmetric to the y-intercept across the axis of symmetry.īecause (0, 8) is point on the parabola 2 units to the left of the axis of symmetry, x = 2, (4, 8) will be a point on the parabola 2 units to the right of the axis of symmetry. Substitute the value of h for x into the equation to find the y-coordinate of the vertex, k :įind the axis of symmetry of the quadratic function.Īxis of symmetry of a quadratic function can be determined by the x-coordinate of the vertex. The x-coordinate of the vertex can be determined by (h, k) = (4, -4) Graphing a Quadratic Function in Standard Formįind the vertex of the quadratic function. So, the vertex of the given quadratic function is Substitute the value of h into the equation for x to find k, the y-coordinate of the vertex. Solve for h, the x-coordinate of the vertex. The vertex of a quadratic function is (h, k), so to determine the x-coordinate of the vertex, solve b = -2ah for h.īecause h is the x-coordinate of the vertex, we can use this value to find the y-value, k, of the vertex.įind the vertex of the quadratic function : The equation y = ax 2 - 2axh + ah 2 + k is a quadratic function in standard form with Write the vertex form of a quadratic function. Using Vertex Form to Derive Standard Form Where a, b and c are real numbers, and a ≠ 0. The standard form of a quadratic function is
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