So we get negative four is equal to eight times two squared.
We have that negative five plus seven is equal to two. And now all that’s left to do is simplify and rearrange to solve for the value of ?. We get negative four is equal to ? times negative five plus seven all squared. So we substitute these coordinates into the equation for our graph. We can find one such point with coordinates negative five, negative four. And when choosing this point, we should choose a point with integer coordinates, since then we can be accurate. And to do this, we’re going to need the coordinates of a point which lies on the line. This gives us ? is equal to ? times ? minus negative seven all squared plus zero, which we can simplify to give us ? is equal to ? times ? plus seven all squared. To do this, let’s first substitute ℎ is negative seven and ? is equal to zero into the vertex form. The only unknown left in the vertex form is the value of ?. Therefore, we’ve determined the values of both ℎ and ?. Therefore, since we found the coordinates of the vertex to be negative seven, zero, we know ℎ must be negative seven and ? must be zero. And this is because for a quadratic equation given in vertex form, the coordinates of the vertex will be ℎ, ?. In this case, we can see the coordinates of this point are negative seven, zero.Īnd since we can determine the coordinates of the vertex of this graph, it will be easier to work with the vertex form. Or alternatively, since this curve opens downwards, it will be the maximum value for the output. And remember, this is the point on the curve where the line of symmetry passes through. However, a good rule of thumb is to check what the coordinates of the vertex of the graph is. And there are positives and negatives to choosing either. The first of these is called the standard form for a quadratic equation, and the second is called the vertex form. We can write this in the form ? is equal to ?? squared plus ?? plus ? or ? is equal to ? times ? minus ℎ all squared plus ?, where ?, ?, ?, ℎ, and ? are real numbers and ? is not allowed to be equal to zero. And to do this, we’ll start by recalling there’s two ways we can represent the graph of a quadratic function. And we need to determine the quadratic equation which is represented by this graph. In this question, we’re given the graph of a function. Write the quadratic equation represented by the graph shown.