Nicole drops the ball from 4 feet above the ground, so the point representing the \(y\)-intercept is \((0,4)\). Since the value of \(c\) in the expanded equation is 4, the \(y\)-intercept is 4. Since both binomials are the same, there is one solution, which is 2. Next, set each binomial equal to 0 and solve for \(x\). Start by writing the quadratic equation as two binomials. Since the length of the flag is 4 feet longer than its width, the length of the flag is 12 feet. Therefore, the width of the flag is 8 feet. Since this problem is about the area of a flag, the negative solution, -12, does not apply to this scenario. Plot the vertex and the \(x\)-intercepts onto the coordinate plane and join the points with a smooth curve.
The vertex of this function is \((-2,-100)\). Substitute -2 into the quadratic equation for \(w\) and simplify: This MATHguide video demonstrates how to solve quadratic equations by method of graphing. Next, find \(k\), which is the vertex’s \(y\)-coordinate. Divide the sum of the \(x\)-intercepts by 2: Start by finding \(h\), which is the vertex’s \(x\)-coordinate. Now that we know the \(x\)-intercepts, find the coordinates for the vertex, \((h,k)\). The graph of the function passes through the \(x\)-axis at -12 and 8. These numbers are 12 and -8.įrom here, equate each binomial to 0 and solve for \(w\). Factor the equation by finding two numbers that result in a sum of 4 and a product of -96. Then, identify the coordinates for the \(x\)-intercepts. Write the quadratic equation in standard form. Next, simplify the equation by distributing \(w\). Since the length of the flag is 4 feet longer than its width, use \(w+4\) to represent the length. Since the width is not known, use w to represent width. Substitute the values from the word problem into this formula. Start by recalling the formula for the area of a rectangle, which is length times width. The vertex is the point on the parabola where the graph intersects its axis of symmetry. However, all parabolas share the same U-shape.Ī parabola is symmetric over an invisible line called the axis of symmetry. The parabola can open upward or downward and can vary in width. The graph of a quadratic function is a two-dimensional curve called a parabola. First, a quadratic function is a polynomial function, and its highest degree term is of the second degree. We’ll also talk about how to graph a quadratic equation and analyze the graph to find solutions.īefore we get started, let’s review a few things. Hello, and welcome to this video about solutions of a quadratic on a graph! Today we’ll learn how to find solutions to a quadratic function by looking at its graph. Solution: First, convert the given equation into the standard form, (3x2-11x+50).