Substitute the x-value into the original expression to determine, if the corresponding y-value is positive or negative. To find zeros, set the quadratic expression x 2 - 2x - 3 equal to 0. The y-values of quadratic function will either turn from positive to negative or from negative to positive, when the graph crosses the x-axis.įind the zeros of the function to identify these points. Identify the intervals on which the quadratic function Determine Positive and Negative Intervals Hence, the ball will take 5 seconds to hit the ground. Because time can never be a negative value. When the ball hits the ground, height "h" = 0. The height of the ball "h" from the ground at time "t" seconds is given by, h = -16t 2 + 64t + 80.How long will the ball take to hit the ground? It will reach a maximum vertical height and then fall back to the ground. X = 2 / 3 or x = 4 Find the Zeros of a Quadratic FunctionĪ ball is thrown upwards from a rooftop which is above from the ground. Solve the following quadratic equation by factoring : To use the Zero Product Property, rewrite the equation, so that it is an expression equals to 0, then factor and solve. In the case of two factors, if pq = 0, then either The Zero Product Property states that if a product of real-number factors is 0, then at least one of the factors must be 0. The factors, (x + 4) and (x - 2), are related to the zerosīecause each of the zeros make one of the factors 0. Substitute x = -4 and x = 2 into the factored form of the equation. So the zeros of the function are x = -4 and x = 2. The x-intercepts of the graph are -4 and 2. The factors of -8 have a sum of 2 are -2 and 4. The expression x 2 + 2x - 8 can be expressed as a product of two factors. How do the zeros of the function relate to the factors of the expression x 2 + 2x - 8 ? The graph shows the function defined by y = x 2 + 2x - 8. Using (+3) and (-6), factor the given quadratic expression.į(x) = (2x + 3)(x - 3) Relate Factors to Zeros of a Function Multiply the coefficient of x 2, 2 by the constant term -9.įactor -18 into two parts such that sum of the two parts is equal to the coefficient of x, -3 and the product is equal to -18. Therefore, the factored form of the given quadratic function is (()() 0) By the zero-factor property, at least one of the factors must be zero, so, set each of the factors equal to 0 and solve for the variable. (ax2 + bx + c 0) Factor the quadratic expression. Using (-2) and (-3), factor the given quadratic expression. Set the equation equal to zero, that is, get all the nonzero terms on one side of the equal sign and 0 on the other. Multiply the coefficient of x 2, 1 by the constant term 14.įactor 6 into two parts such that sum of the two parts is equal to the coefficient of x, -5 and the product is equal to 6. Write the following quadratic function in factored form. The factored form of a quadratic function is
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