Lesson 24 - Unit 7 - Algebra 1 - Illustrative Mathematics

The graphs that represent a linear function and a quadratic function are shown here.

The quadratic function is defined by 2x^{2}-5x.

Find the coordinates of R without using graphing technology. Show your reasoning.

Diego finds his neighbor's baseball in his yard, about 10 feet away from a five-foot fence. He wants to return the ball to his neighbors, so he tosses the baseball in the direction of the fence.

Function h, defined by h(x)=-0.078x^{2}+0.7x+5.5, gives the height of the ball as a function of the horizontal distance away from Diego.

Does the ball clear the fence? Explain or show your reasoning.

Here are two quadratic functions: f(x)=(x+5)^{2}+\frac{1}{2} and g(x)=(x+5)^{2}+1.

Andre says that both f and g have a minimum value, and that the minimum value of f is less than that of g. Do you agree? Explain your reasoning.

Function p is defined by the equation p(x)=(x+10)^{2}-3.

Function q is represented by this graph.

Which function has the smaller minimum? Explain your reasoning.

Without using graphing technology, sketch a graph that represents each quadratic function. Make sure the x-intercepts, y-intercept, and vertex are plotted accurately.