Question

alyzing equations use the discriminant to match the quadratic equation ( 5 x ^ { 2 } - 10 x - 35 = 0 ) with the correct graph.
the discriminant is. this means that the graph has x - intercepts. the y - intercept is.

Explanation:

Step1: Find the discriminant

For a quadratic equation \(ax^{2}+bx + c=0\), the discriminant is \(D=b^{2}-4ac\).
In the equation \(5x^{2}-10x - 35 = 0\), \(a = 5\), \(b=-10\), \(c=-35\).

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Step2: Determine the number of \(x\)-intercepts

Since \(D = 800>0\), the quadratic equation has two distinct real roots. So the graph has two \(x\)-intercepts.

Step3: Find the \(y\)-intercept

To find the \(y\)-intercept, set \(x = 0\) in the equation \(y=5x^{2}-10x - 35\).
When \(x = 0\), \(y=-35\).

Answer:

The discriminant is \(800\). This means that the graph has two \(x\)-intercepts. The \(y\)-intercept is \(-35\).